10/18/2017 HW Sec. 1.5-2
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Current Score : 11 / 22 Due : Thursday, October 19 2017 10:59 PM EDT
HW Sec. 1.5-2 (Homework)
Janean Owens MTH-151, section 90, Fall 2017 Instructor: Mushtaq Khan
WebAssign
10/18/2017 HW Sec. 1.5-2
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1. 4/4 points | Previous AnswersLarATRMRP7 1.5.062.
The function g is related to one of the six parent functions.
(a) Identify the parent function f. f(x) =
|x|
(b) Describe the sequence of transformations from f to g. (Select all that apply.)
(c) Sketch the graph of g by hand.
g(x) = |x − 3| − 41 2
horizontal shift of 3 units to the left
horizontal shrink
horizontal shift of 3 units to the right
vertical shrink
vertical shift of 4 units upward
vertical shift of 4 units downward
10/18/2017 HW Sec. 1.5-2
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(d) Use function notation to write g in terms of the parent function f.
g(x) = − f(x − 3) + 41 2
g(x) = − f(x − 3) − 41 2
g(x) = f(x − 3) − 41 2
g(x) = f(x + 3) − 41 2
g(x) = f(x − 3) + 41 2
g(x) = − f(x + 3) − 41 2
10/18/2017 HW Sec. 1.5-2
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2. 0/1 points | Previous AnswersLarATRMRP7 1.5.074.
Consider the graph below.
Determine which equation(s) may be represented by the graph shown. (Select all that apply.)
3. 0/1 points | Previous AnswersLarATRMRP7 1.5.076.
Consider the graph below.
Determine which equation(s) may be represented by the graph shown. (Select all that apply.)
f(x) = -(x − 2)3 + 4
f(x) = -(x + 4)3 + 2
f(x) = (x + 4)3 + 2
f(x) = (-x + 4)3 + 2
f(x) = (-x − 4)3 + 2
f(x) = -(x − 4)3 + 2
10/18/2017 HW Sec. 1.5-2
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4. 1/1 points | Previous AnswersLarATRMRP7 1.5.502.XP.
Sketch the graphs of the three functions by hand on the same rectangular coordinate system. Verify your results with a graphing utility.
f(x) = x2
g(x) = x2 − 3 h(x) = (x + 5)2 + 4
Submission Data
10/18/2017 HW Sec. 1.5-2
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5. 1/1 points | Previous AnswersLarATRMRP7 1.5.503.XP.
Sketch the graphs of the three functions by hand on the same rectangular coordinate system. Verify your results with a graphing utility.
f(x) = |x| g(x) = |x + 1| h(x) = −2|x + 2| − 4
10/18/2017 HW Sec. 1.5-2
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6. 1/1 points | Previous AnswersLarATRMRP7 1.5.504.XP.
Sketch the graphs of the three functions by hand on the same rectangular coordinate system. Verify your results with a graphing utility.
f(x) =
g(x) =
h(x) = −
x
1 3
x
x + 5
10/18/2017 HW Sec. 1.5-2
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7. 4/4 points | Previous AnswersLarATRMRP7 1.5.505.XP.
The function g is related to one of the six parent functions.
(a) Identify the parent function f. f(x) =
x2
(b) Describe the sequence of transformations from f to g. (Select all that apply.)
(c) Sketch the graph of g by hand.
g(x) = −(x + 7)2 + 5
reflection in the y-axis
horizontal shift of 7 units to the right
reflection in the x-axis
vertical shift of 5 units upward
horizontal shift of 7 units to the left
10/18/2017 HW Sec. 1.5-2
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(d) Use function notation to write g in terms of the parent function f.
g(x) = f(x + 7) + 5
g(x) = −f(x − 7) + 5
g(x) = −f(x + 7) − 5
g(x) = f(x − 7) + 5
g(x) = f(x + 7) − 5
g(x) = −f(x + 7) + 5
10/18/2017 HW Sec. 1.5-2
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8. –/4 pointsLarATRMRP7 1.5.506.XP.
The function g is related to one of the six parent functions.
(a) Identify the parent function f. f(x) =
(b) Describe the sequence of transformations from f to g. (Select all that apply.)
vertical shrink
vertical shift of 6 units downward
reflection in the x-axis
horizontal shift of 6 units to the left
horizontal shrink
vertical shift of 6 units upward
(c) Sketch the graph of g by hand.
g(x) = − (x + 6)31 2
10/18/2017 HW Sec. 1.5-2
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(d) Use function notation to write g in terms of the parent function f.
g(x) = f(x + 6)1 2
g(x) = − f(x − 6)1 2
g(x) = − f(x) + 61 2
g(x) = − f(x + 6)1 2
g(x) = f(x) − 61 2
g(x) = f(x) + 61 2
10/18/2017 HW Sec. 1.5-2
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9. –/4 pointsLarATRMRP7 1.5.507.XP.
The function g is related to one of the six parent functions.
(a) Identify the parent function f. f(x) =
(b) Describe the sequence of transformations from f to g. (Select all that apply.)
reflection in the x-axis
vertical shift of 2 units downward
horizontal shift of 1 units to the right
horizontal shrink
horizontal shift of 1 units to the left
vertical shift of 2 units upward
(c) Sketch the graph of g by hand.
g(x) = − − 2x + 1
10/18/2017 HW Sec. 1.5-2
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(d) Use function notation to write g in terms of the parent function f.
g(x) = f(x − 1) − 2
g(x) = −f(x − 1) + 2
g(x) = f(x + 1) − 2
g(x) = f(x − 1) + 2
g(x) = −f(x + 1) + 2
g(x) = −f(x + 1) − 2
10/18/2017 HW Sec. 1.5-2
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10.–/1 pointsLarATRMRP7 1.5.VE.001.
Watch the video below then answer the question.
Use vertical and horizontal shifts to sketch graphs of functions
View Transcript
Describe the graph of y = x6 − 9 in terms of shifting the graph of y = x6.
The graph of y = x6 is shifted up vertically 9 units.
The graph of y = x6 is shifted right horizontally 9 units.
The graph of y = x6 is shifted down vertically 9 units.
The graph of y = x6 is shifted left horizontally 9 units.
none of the above
Decision Analysis Case Study: Valley of the Sun Reviews
Valley of the Sun Academy (VSA) is an online school specializing in GED programs for the Phoenix area. Valley of the Sun Academy enrolls 813 students and has a part-time faculty pool of 65 online instructors.
Online faculty are reviewed annually and provided with feedback about their facilitation techniques, content expertise, engagement, and classroom management. If necessary, remediation and additional support are provided by the Faculty Advisory Board (FAB). The online faculty reviews are one factor used to determine overall performance, teaching status, and potential performance appraisals.
Recently, the FAB submitted a proposal for a new approach for the next fiscal year, the Peer Faculty Performance Review (PFPR). Human Resources (HR) and the school’s chief financial officer are evaluating the suggestion against the current design, described by VSA’s director. Both review processes are outlined below.
Current Design
Valley of the Sun Academy uses an external firm, TeachBest Consulting, to conduct annual reviews for online faculty. The review team is composed of faculty members at other online institutions, including universities and high schools. Valley of the Sun Academy faculty are not part of the review process, and TeachBest Consulting handles hiring and training internally. Valley of the Sun Academy’s HR department assigns completed courses to review, and VSA’s Technical Support team is responsible for providing access.
Once completed, the TeachBest consultant submits the review form to VSA’s HR department, and HR submits a payment for each review. In addition, VSA has an annual contract with TeachBest Consulting.
The overall contract is $2,500/year. If VSA’s enrollment reaches 1,000 or more students or their faculty pool expands to 75 or more instructors, the contract amount will increase to $5,000/year. There is a 75% chance the student enrollment will reach 1,000 students within the next 18 months and a 25% chance enrollment will not increase. During the next nine months, Human Resources anticipates hiring at least six math instructors.
Individual reviewers are paid $75 for each review. Reviews are conducted in March, July, and November, with all faculty reviewed by December 1.
Valley of the Sun Academy is responsible for disseminating the results of the review to faculty members. If questions arise about review results, the FAB is responsible for verifying the review and responding to the instructor. Periodically, the Faculty Advisory Board finds fault with the initial review and follow-up must be scheduled. Each year, about 5% of the initial reviews are found to be inaccurate and new reviews must be scheduled. Valley of the Sun Academy pays a discounted price of $50 for each follow-up review.
Peer Faculty Performance Review (PFPR) Proposal
The FAB proposes to conduct faculty reviews in-house and no longer contract TeachBest Consulting. Human Resources will review faculty files and invite the top three performing instructors in four disciplines (Literacy and Communication, Social Sciences, Math, and Science and Technology) to join the PFPR committee.
Initial responsibilities will involve creating a new review form and conducting a norming session for consistency. There will be ongoing technology fees of $20/month for each reviewer, to ensure access to create and complete the review forms. There will also be an initial cost to set up the norming session. The Faculty Advisory Board recommends one of three options:
1. A $500 session that can be scheduled at any time with TeachBest Consulting.
2. A $750 session offered monthly by an external employee development firm.
3. A session designed by VSA’s HR and instructional design specialists, which would be free to attend but would require internal time and labor costs; HR anticipates a start of two months from implementation would prevent interrupting normal business practices.
Because the responsibilities are not included in current faculty contracts, FAB recommends stipends of $50 for each review completed. With the new internal PFPR process, FAB anticipates faculty reviews would no longer be overturned and there would not be a need to conduct secondary reviews. Additionally, FAB expects reviews to move to a 9-month rolling cycle rather than once every academic year.
© 2016. Grand Canyon University. All Rights Reserved.
2
Review "Decision Analysis Case Study: Valley of the Sun Reviews" for this topic's case study, a proposal to change the faculty performance review process at Valley of the Sun Academy (VSA).
Based on the information presented in the case study, create a decision tree or Excel-based analysis to determine the most appropriate recommendation.
In a 500-750-word report to VSA's Human Resources department and the chief financial officer, explain your approach and the rationale for this method. Evaluate both outcomes and how they would be applied to this decision. Conclude your report with your recommendation for the review process VSA should adopt.
Submit your Excel-based analysis or decision tree with your report.
Prepare the assignment according to the guidelines found in the APA Style Guide, located in the Student Success Center. An abstract is not required.
10/18/2017 HW Sec 1.4-2
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Current Score : 3 / 38 Due : Thursday, October 19 2017 11:59 PM EDT
1. –/1 pointsLarATRMRP7 1.4.062.
Sketch the graph of the piecewise-defined function.
2. 1/1 points | Previous AnswersLarATRMRP7 1.4.068.
Use a graphing utility to graph the function and determine whether it is even, odd, or neither.
HW Sec 1.4-2 (Homework)
Janean Owens MTH-151, section 90, Fall 2017 Instructor: Mushtaq Khan
WebAssign
h(x) = 5 + x if x < 0 x2 + 3 if x ≥ 0
f(x) = −x2 − 4
The function is even.
The function is odd.
The function is neither even nor odd.
10/18/2017 HW Sec 1.4-2
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3. 1/1 points | Previous AnswersLarATRMRP7 1.4.070.
Use a graphing utility to graph the function and determine whether it is even, odd, or neither.
4. 1/1 points | Previous AnswersLarATRMRP7 1.4.072.
Use a graphing utility to graph the function and determine whether it is even, odd, or neither. (Use only inclusive endpoints in your graph.)
5. –/4 pointsLarATRMRP7 1.4.074.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Consider the following.
Exercise (a) Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. Exercise (b) Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd.
g(t) = t − 4 3
The function is even.
The function is odd.
The function is neither even nor odd.
f(x) = −|x − 2|
The function is even.
The function is odd.
The function is neither even nor odd.
− , −24 5
10/18/2017 HW Sec 1.4-2
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6. –/4 pointsLarATRMRP7 1.4.076.
Consider the following.
(2, −8)
(a) Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. (x, y) = ( , ) (b) Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. (x, y) = ( , )
10/18/2017 HW Sec 1.4-2
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7. –/7 pointsLarATRMRP7 1.4.080.
Determine whether the function is even, odd, or neither algebraically, graphically by using a graphing utility to graph the function, and numerically by using the table feature of the graphing utility to compare f(x) and f(−x) for several values of x.
(a) algebraically f(−x) = f(x)
f(−x) = −f(x)
neither of these
(b) graphically
(c) numerically (If the answer is not a number, enter NAN.)
=
=
=
=
Determine whether the function is even, odd, or neither. The function is even.
The function is odd.
The function is neither even nor odd.
f(x) = x4 − 2x2 + 4
f(3)
f(−3)
f(9)
f(−9)
10/18/2017 HW Sec 1.4-2
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8. –/2 pointsLarATRMRP7 1.4.090.
Graph the function and determine the interval(s) for which
Interval(s) for which f(x) ≥ 0: (Enter your answer using interval notation.)
9. –/1 pointsLarATRMRP7 1.4.098.
Determine whether the statement is true or false.
It is possible for an odd function to have the interval [0, ∞) as its domain. True
False
f(x) ≥ 0.
f(x) = x2 − 4x
10/18/2017 HW Sec 1.4-2
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10.–/8 pointsLarATRMRP7 1.4.110.
Half of the graph of an odd function is shown.
(a) Sketch a complete graph of the function.
10/18/2017 HW Sec 1.4-2
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(b) Find the domain and range of the function. (Enter your answers using interval notation.)
(c) Identify the open intervals on which the function is increasing, decreasing, or constant. (Enter your answers using interval notation. If an answer does not exist, enter DNE. Assume all critical points occur at integer values.)
increasing
decreasing
constant
(d) Find any relative minimum and relative maximum values of the function. (If an answer does not exist, enter DNE. Assume all
domain
range
10/18/2017 HW Sec 1.4-2
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critical values occur at integer values.)
relative minimum (x, y) =
relative maximum (x, y) =
10/18/2017 HW Sec 1.4-2
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11.–/4 pointsLarATRMRP7 1.4.502.XP.
Consider the following.
(a) Use a graphing utility to graph the function.
(b) Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
increasing
decreasing
constant
f(x) = 3 − x
10/18/2017 HW Sec 1.4-2
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12.–/1 pointsLarATRMRP7 1.4.504.XP.
Sketch the graph of the piecewise-defined function.
f(x) = {(x + 4 text(, ) x <= -3, 2x - 2 text(, ) x>-3)
10/18/2017 HW Sec 1.4-2
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13.–/1 pointsLarATRMRP7 1.4.505.XP.
Sketch the graph of the piecewise-defined function.
f(x) = {(x + 8 text(, ) x <= -3, -6 text(, ) -3 < x < 1, 5x - 3 text(, ) x>=1)
14.–/1 pointsLarATRMRP7 1.4.506.XP.
Use a graphing utility to graph the function and determine whether it is even, odd, or neither.
The function is even.
The function is odd.
The function is neither even nor odd.
f(x) = 5 − 3x
10/18/2017 HW Sec 1.4-2
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15.–/1 pointsLarATRMRP7 1.4.VE.003.
Watch the video below then answer the question.
Even and Odd Functions
View Transcript
Determine from the list the functions that are neither even nor odd. (Select all that apply.)
10/18/2017 HW Sec. 1.5-1
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Current Score : 13 / 40 Due : Thursday, October 19 2017 10:59 PM EDT
1. 1/1 points | Previous AnswersLarATRMRP7 1.5.002.
Match the rigid transformation of y = f(x) with the correct representation of the graph of h, where c > 0.
h(x) = f(x) − c vertical shift c units downward
h(x) = f(x + c) horizontal shift c units to the left
h(x) = f(x) + c vertical shift c units upward
h(x) = f(x − c) horizontal shift c units to the right
2. 2/2 points | Previous AnswersLarATRMRP7 1.5.003.
Fill in the blanks.
A reflection in the x-axis of y = f(x) is represented by h(x) = −f(x) , while a reflection in the y-axis of y = f(x) is represented by h(x) = f(−x) .
3. 2/2 points | Previous AnswersLarATRMRP7 1.5.004.
Fill in the blanks.
A nonrigid transformation of represented by is a vertical stretch when c > 1 and a vertical shrink when 0 < c < 1 .
HW Sec. 1.5-1 (Homework)
Janean Owens MTH-151, section 90, Fall 2017 Instructor: Mushtaq Khan
WebAssign
y = f(x) cf(x)
10/18/2017 HW Sec. 1.5-1
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4. –/1 pointsLarATRMRP7 1.5.010.
Sketch the graphs of the three functions by hand on the same rectangular coordinate system. Verify your results with a graphing utility.
f(x) = (x − 5)2
g(x) = (x + 5)2 + 5 h(x) = −(x − 5)2 − 2
10/18/2017 HW Sec. 1.5-1
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5. –/1 pointsLarATRMRP7 1.5.012.
Sketch the graphs of the three functions by hand on the same rectangular coordinate system. Verify your results with a graphing utility.
f(x) = x2
g(x) = x2 + 4
h(x) = − x2
1 3
1 3
10/18/2017 HW Sec. 1.5-1
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6. 3/7 points | Previous AnswersLarATRMRP7 1.5.020.
Use the graph of f to sketch each graph.
(a)
(b)
y = f(x) − 1
y = f(x + 2)
10/18/2017 HW Sec. 1.5-1
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(c)
(d)
y = f(x − 1)
y = −f(x − 2)
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(e)
(f)
y = f(−x)
y = f(x)1 2
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(g)
y = f(2x)
10/18/2017 HW Sec. 1.5-1
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7. 1/1 points | Previous AnswersLarATRMRP7 1.5.024.
Compare the graph of the function with the graph of its parent function.
8. 1/1 points | Previous AnswersLarATRMRP7 1.5.026.
Compare the graph of the function with the graph of its parent function.
9. 1/1 points | Previous AnswersLarATRMRP7 1.5.028.
Compare the graph of the function with the graph of its parent function.
y = − 81 x
is shifted to the right 8 units.
is horizontally stretched 8 fold.
is shifted down 8 units.
is shifted to the left 8 units.
is vertically stretched 8 fold.
y = − 8 1 x
f(x) = 1 x
y = − 8 1 x
f(x) = 1 x
y = − 8 1 x
f(x) = 1 x
y = − 8 1 x
f(x) = 1 x
y = − 8 1 x
f(x) = 1 x
y = |x + 2|
y = |x + 2| is f(x) = |x| horizontally stretched 2 fold.
y = |x + 2| is f(x) = |x| vertically stretched 2 fold.
y = |x + 2| is f(x) = |x| shifted up 2 units.
y = |x + 2| is f(x) = |x| shifted to the right 2 units.
y = |x + 2| is f(x) = |x| shifted to the left 2 units.
y = x − 4
is shifted up 4 units.
is shifted to the left 4 units.
is shifted to the right 4 units.
is horizontally stretched 4 fold.
is shifted down 4 units.
y = x − 4 f(x) = x
y = x − 4 f(x) = x
y = x − 4 f(x) = x
y = x − 4 f(x) = x
y = x − 4 f(x) = x
10/18/2017 HW Sec. 1.5-1
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10.–/3 pointsLarATRMRP7 1.5.032.MI.
Consider the following graph.
Identify the parent function and describe the transformation shown in the graph. (Select all that apply.) y =
horizontal shift of 3 units to the left
vertical shift of 3 units downward
vertical shift of 3 units upward
reflection in the x-axis
vertical stretch
horizontal shift of 3 units to the right
Write an equation for the graphed function. y =
10/18/2017 HW Sec. 1.5-1
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11.–/3 pointsLarATRMRP7 1.5.030.
Consider the following graph.
Identify the parent function and the transformation shown in the graph. (Select all that apply.) y =
A horizontal shift of three units to the left.
A horizontal shift of three units to the right.
A vertical shift of three units downward.
A vertical stretch, three-fold.
A vertical shift of three units upward.
Write an equation for the graphed function. y =
10/18/2017 HW Sec. 1.5-1
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12.–/3 pointsLarATRMRP7 1.5.034.
Consider the following graph.
Identify the parent function and the transformation shown in the graph. (Select all that apply.) y =
A reflection in the x-axis.
A vertical stretch, two-fold.
A horizontal shift of two units to the left.
A vertical shift of two units upward.
A horizontal shift of two units to the right.
A horizontal stretch, two-fold.
Write an equation for the graphed function. y =
13.1/1 points | Previous AnswersLarATRMRP7 1.5.036.
Compare the graph of the function with the graph of its parent function.
y = |−x|
The graph of y = |−x| is identical to the graph of f(x) = |x|.
The graph of y = |−x| is a vertical shrink of f(x) = |x|.
The graph of y = |−x| is a reflection about the origin of the graph of f(x) = |x|.
The graph of y = |−x| is a reflection in the x-axis.
The graph of y = |−x| is a reflection about either axis of the graph of f(x) = |x|, as −f(x) = f(−x).
10/18/2017 HW Sec. 1.5-1
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14.1/1 points | Previous AnswersLarATRMRP7 1.5.038.
Compare the graph of the function with the graph of its parent function.
15.–/1 pointsLarATRMRP7 1.5.040.
Compare the graph of the function with the graph of its parent function.
The graph of is only a reflection about the y-axis, compared to the graph of
The graph of is a reflection about the origin of the graph of
The graph of is identical to the graph of
The graph of is only a reflection about the x-axis, compared to the graph of
The graph of is a reflection about either axis of the graph of as −f(x) = f(−x).
16.–/1 pointsLarATRMRP7 1.5.042.
Compare the graph of the function with the graph of its parent function.
y = −x3
The graph of y = −x3 is only a reflection about the y-axis, compared to the graph of f(x) = x3.
The graph of y = −x3 is a reflection about either axis of the graph of f(x) = x3, as −f(x) = f(−x).
The graph of y = −x3 is identical to the graph of f(x) = x3.
The graph of y = −x3 is a reflection about the origin of the graph of f(x) = x3.
The graph of y = −x3 is only a reflection about the x-axis compared to the graph of f(x) = x3.
y = − 1 x
y = − 1 x
y = .1 x
y = − 1 x
f(x) = .1 x
y = − 1 x
f(x) = .1 x
y = − 1 x
y = .1 x
y = − 1 x
f(x) = ,1 x
p(x) = x21 2
p(x) = x2 is a reflection about the x-axis of f(x) = x2.1 2
p(x) = x2 is a reflection about the y-axis of f(x) = x2.1 2
p(x) = x2 is a vertical shrink of f(x) = x2.1 2
p(x) = x2 is identical to f(x) = x2.1 2
p(x) = x2 is a vertical stretch of f(x) = x2.1 2
10/18/2017 HW Sec. 1.5-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738222 13/17
17.–/1 pointsLarATRMRP7 1.5.044.
Compare the graph of the function with the graph of its parent function.
is a reflection about the x-axis of
is a vertical shrink of
is a reflection about the y-axis of
is identical to the graph of
is a vertical stretch of
18.–/1 pointsLarATRMRP7 1.5.046.
Compare the graph of the function with the graph of its parent function.
The graph of is a reflection about the y-axis of the graph of f(x) = |x|.
The graph of is identical to the graph of f(x) = |x|.
The graph of is a vertical stretch of the graph of f(x) = |x|.
The graph of is a horizontal stretch of the graph of f(x) = |x|.
The graph of is a reflection about the x-axis of the graph of f(x) = |x|.
y = 8 x
y = 8 x f(x) = .x
y = 8 x f(x) = .x
y = 8 x f(x) = .x
y = 8 x f(x) = .x
y = 8 x f(x) = .x
y = x1 5
y = x 1 5
y = x 1 5
y = x 1 5
y = x 1 5
y = x 1 5
10/18/2017 HW Sec. 1.5-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738222 14/17
19.–/4 pointsLarATRMRP7 1.5.054.
The function g is related to one of the six parent functions.
(a) Identify the parent function f. f(x) =
(b) Describe the sequence of transformations from f to g. (Select all that apply.)
vertical stretch
horizontal shift of 3 units to the right
reflection in the y-axis
vertical shrink
vertical shift of 4 units downward
horizontal shift of 3 units to the left
reflection in the x-axis
(c) Sketch the graph of g by hand.
g(x) = − (x + 3)2 − 41 4
10/18/2017 HW Sec. 1.5-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738222 15/17
(d) Use function notation to write g in terms of the parent function f.
g(x) = − f(x + 3) + 41 4
g(x) = f(x + 3) − 41 4
g(x) = − f(x − 3) − 41 4
g(x) = − f(x + 3) − 41 4
g(x) = f(x − 3) − 41 4
g(x) = f(x + 3) + 41 4
10/18/2017 HW Sec. 1.5-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738222 16/17
20.–/4 pointsLarATRMRP7 1.5.058.
The function g is related to one of the six parent functions.
(a) Identify the parent function f. f(x) =
(b) Describe the sequence of transformations from f to g.
A horizontal shift 3 units to the right, a reflection in the x-axis, and a vertical shift 7 units downward.
A horizontal shift 3 units to the left, a reflection in the x-axis, and a vertical shift 7 units upward.
A horizontal shift 3 units to the left, a reflection in the x-axis, and a vertical shift 7 units downward.
A horizontal shift 3 units to the right, a reflection in the x-axis, and a vertical shift 7 units upward.
A horizontal shift 3 units to the left, a reflection in the y-axis, and a vertical shift 7 units downward.
(c) Sketch the graph of g by hand.
g(x) = −(x + 3)3 − 7
10/18/2017 HW Sec. 1.5-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738222 17/17
(d) Use function notation to write g in terms of the parent function f.
g(x) = −f(x + 3) − 7
g(x) = f(x + 3) + 7
g(x) = −f(x + 3) + 7
g(x) = f(x + 3) − 7
g(x) = f(x − 3) − 7
g(x) = −f(x − 3) − 7
10/18/2017 HW Sec 1.4
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738220 1/11
Current Score : – / 41 Due : Thursday, October 19 2017 11:59 PM EDT
1. –/1 pointsLarATRMRP7 1.4.001.
Fill in the blank.
A function f is ---Select--- on an interval when, for any x1 and x2 in the interval, x1 < x2 implies
2. –/1 pointsLarATRMRP7 1.4.002.
Fill in the blank.
A function f is ---Select--- when, for each x in the domain of
3. –/1 pointsLarATRMRP7 1.4.004.
A vertical line intersects a graph twice. Does the graph represent a function? Yes
No
4. –/1 pointsLarATRMRP7 1.4.005.
Let f be a function such that for all values of x in the interval (0, 3). Does f(2) represent a relative minimum or a relative maximum?
relative minimum
relative maximum
neither
HW Sec 1.4 (Homework)
Janean Owens MTH-151, section 90, Fall 2017 Instructor: Mushtaq Khan
WebAssign
f(x1) > f(x2).
f, f(−x) = f(x).
f(2) ≥ f(x)
10/18/2017 HW Sec 1.4
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738220 2/11
5. –/3 pointsLarATRMRP7 1.4.008.
Consider the graph below.
Use the graph of the function to find the domain of f. (Enter your answer using interval notation.)
Use the graph of the function to find the range of f. (Enter your answer using interval notation.)
Find
f(1).
10/18/2017 HW Sec 1.4
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738220 3/11
6. –/3 pointsLarATRMRP7 1.4.010.
Consider the graph below.
Use the graph of the function to find the domain of f. (Enter your answer using interval notation.)
Use the graph of the function to find the range of f. (Enter your answer using interval notation.)
Find f(0).
7. –/2 pointsLarATRMRP7 1.4.014.
Use a graphing utility to graph the function and estimate its domain and range. Then find the domain and range algebraically. (Enter your answers using interval notation.)
domain
range
h(t) = 4 − t2
10/18/2017 HW Sec 1.4
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738220 4/11
8. –/11 pointsLarATRMRP7 1.4.018.
Use the graph of the function to answer the questions.
(a) Determine the domain of the function. (Enter your answer using interval notation.)
(b) Determine the range of the function. (Enter your answer using interval notation.)
(c) Find the value(s) of x for which (Enter your answers as a comma-separated list.) x =
(d) What are the values of x from part (c) referred to graphically?
x-intercepts
y-intercepts
solutions
local maxima
local minima
(e) Find f(0), if possible. (If an answer does not exist, enter DNE.) f(0) = (f) What is the value from part (e) referred to graphically?
f(x) = x + 4, 4 − x2,
x ≤ 0 x > 0
f(x) = 0.
10/18/2017 HW Sec 1.4
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738220 5/11
x-intercept
local maximum
local minimum
solution
y-intercept
(g) What is the value of f at f = What are the coordinates of the point?
(h) What is the value of f at f = What are the coordinates of the point?
(i) The coordinates of the point on the graph of f at which can be labeled or
x = 1?
(x, y) =
x = −1?
(x, y) =
x = −2 (−2, f(−2)), −2, .
10/18/2017 HW Sec 1.4
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738220 6/11
9. –/2 pointsLarATRMRP7 1.4.020.
Consider the following.
Use the Vertical Line Test to determine whether y is a function of x. Yes, y is a function of x.
No, y is not a function of x.
Solve for y to describe how you can use a graphing utility to produce the given graph.
x −y2 = 4
y = ±
10/18/2017 HW Sec 1.4
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738220 7/11
10.–/2 pointsLarATRMRP7 1.4.022.
Consider the following.
Use the Vertical Line Test to determine whether y is a function of x. Yes, y is a function of x.
No, y is not a function of x.
Solve for y to describe how you can use a graphing utility to produce the given graph.
x2 = 3xy − 2
y =
10/18/2017 HW Sec 1.4
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738220 8/11
11.–/3 pointsLarATRMRP7 1.4.024.
Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
increasing
decreasing
constant
f(x) = x2 − 2x
10/18/2017 HW Sec 1.4
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738220 9/11
12.–/3 pointsLarATRMRP7 1.4.026.
Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
increasing
decreasing
constant
f(x) = x2 − 9
10/18/2017 HW Sec 1.4
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738220 10/11
13.–/4 pointsLarATRMRP7 1.4.030.
Consider the following.
(a) Use a graphing utility to graph the function.
(b) Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
increasing
decreasing
constant
f(x) = −x3/4
10/18/2017 HW Sec 1.4
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738220 11/11
14.–/2 pointsLarATRMRP7 1.4.036.
Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. (Round your answers to two decimal places. If an answer does not exist, enter DNE.)
f(x) = 4x2 − 3x − 7
15.–/2 pointsLarATRMRP7 1.4.038.
Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. (Round your answers to the nearest integer. If an answer does not exist, enter DNE.)
relative minimum (x, y) =
relative maximum (x, y) =
y = x3 − 6x2 + 16
relative minimum (x, y) =
relative maximum (x, y) =
10/18/2017 HW Sec. 1.6-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738224 1/12
Current Score : 1 / 72 Due : Thursday, October 19 2017 10:59 PM EDT
1. 1/1 points | Previous AnswersLarATRMRP7 1.6.002.
Fill in the blank.
The composition of the function f with the function g is (f ∘ g)(x) = f(g(x)).
2. –/1 pointsLarATRMRP7 1.6.008.
Use the graphs of f and g to graph (To graph h(x), use 4 segments each with closed end points on both ends.) WebAssign Plot
HW Sec. 1.6-1 (Homework)
Janean Owens MTH-151, section 90, Fall 2017 Instructor: Mushtaq Khan
WebAssign
h(x) = (f + g)(x).
10/18/2017 HW Sec. 1.6-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738224 2/12
3. –/5 pointsLarATRMRP7 1.6.012.MI.
Find the following. (Simplify your answers completely.)
(a) (f + g)(x) =
(b) (f − g)(x) =
(c) (fg)(x) =
(d) (f/g)(x) =
What is the domain of f/g? (Enter your answer using interval notation.)
f(x) = 7x − 8, g(x) = 6 − x
10/18/2017 HW Sec. 1.6-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738224 3/12
4. –/10 pointsLarATRMRP7 1.6.012.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Consider the following.
f(x) = 2x − 5, g(x) = 1 − x
Exercise (a) Find (f + g)(x). Exercise (b) Find (f − g)(x). Exercise (c) Find (fg)(x). Exercise (d) Find (f/g)(x).
5. –/1 pointsLarATRMRP7 1.6.020.
Evaluate the indicated function for f(x) = x2 − 1 and g(x) = x − 3 algebraically. If possible, use a graphing utility to verify your answer.
(f − g)(-3)
6. –/1 pointsLarATRMRP7 1.6.026.
Evaluate the indicated function for f(x) = x2 − 1 and g(x) = x − 5 algebraically. If possible, use a graphing utility to verify your answer.
(0)f g
10/18/2017 HW Sec. 1.6-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738224 4/12
7. –/1 pointsLarATRMRP7 1.6.034.
Use a graphing utility to graph the functions f, g, and h in the same viewing window.
f(x) = x, g(x) = −x + 4, h(x) = f(x) − g(x)1 4
10/18/2017 HW Sec. 1.6-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738224 5/12
8. –/3 pointsLarATRMRP7 1.6.042.
Consider the functions below.
f(x) = root3(x-1) g(x)=x^3+1
Find each of the following, if possible. (If it is not possible, enter NONE.)
(a) f∘g
(b) g∘f
(c) (f∘g)(0)
10/18/2017 HW Sec. 1.6-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738224 6/12
9. –/3 pointsLarATRMRP7 1.6.046.
Consider the functions below.
Determine the domains of the following. Use a graphing utility to verify your results. (Enter your answers using interval notation.)
(a) Domain of f
(b) Domain of g
(c) Domain of f ∘ g
f(x) = , g(x) = x + 9 x 8
10/18/2017 HW Sec. 1.6-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738224 7/12
10.–/3 pointsLarATRMRP7 1.6.054.
Consider the functions below.
Determine the domains of the following. Use a graphing utility to verify your results. (Enter your answers using interval notation.)
(a) Domain of
(b) Domain of
(c) Domain of
f(x) = , g(x) = x + 1 2
x2 − 1
f
g
f ∘ g
10/18/2017 HW Sec. 1.6-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738224 8/12
11.–/4 pointsLarATRMRP7 1.6.056.
Consider the functions below.
(a) Find each of the following.
f ∘ g =
g ∘ f =
Find the domain of f ∘ g. (Enter your answer using interval notation.)
(b) Use a graphing utility to graph f ∘ g and g ∘ f. Determine whether f ∘ g = g ∘ f.
Yes, they are equal.
No, they are not equal.
f(x) = , g(x) = x3 − 7x + 7 3
10/18/2017 HW Sec. 1.6-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738224 9/12
12.–/13 pointsLarATRMRP7 1.6.062.
Consider the following functions.
(a) Find and
=
=
(b) Determine algebraically whether
Yes, they are equal.
No, they are not equal.
(c) Use a graphing utility to complete a table of values for the two compositions to confirm your answer to part (b).
x
−1
0
1
2
3
f(x) = (x − 5), g(x) = 3x + 51 3
(f ∘ g)(x) (g ∘ f)(x).
(f ∘ g)(x)
(g ∘ f)(x)
(f ∘ g)(x) = (g ∘ f)(x).
(f ∘ g)(x) (g ∘ f)(x)
10/18/2017 HW Sec. 1.6-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738224 10/12
13.–/11 pointsLarATRMRP7 1.6.064.
Consider the following functions.
(a) Find and
=
=
(b) Determine algebraically whether
Yes, they are equal.
No, they are not equal.
(c) Use a graphing utility to complete a table of values for the two compositions to confirm your answer to part (b). (Round your answers to two decimal places.)
x
0
1
2
3
f(x) = x3 − 5, g(x) = x + 11 3
(f ∘ g)(x) (g ∘ f)(x).
(f ∘ g)(x)
(g ∘ f)(x)
(f ∘ g)(x) = (g ∘ f)(x).
(f ∘ g)(x) (g ∘ f)(x)
10/18/2017 HW Sec. 1.6-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738224 11/12
14.–/11 pointsLarATRMRP7 1.6.066.
Consider the following functions.
(a) Find and
=
=
(b) Determine algebraically whether
Yes, they are equal.
No, they are not equal.
(c) Use a graphing utility to complete a table of values for the two compositions to confirm your answer to part (b). (Round your answers to two decimal places.)
x
0
1
2
3
f(x) = , g(x) = −x4 3x − 7
(f ∘ g)(x) (g ∘ f)(x).
(f ∘ g)(x)
(g ∘ f)(x)
(f ∘ g)(x) = (g ∘ f)(x).
(f ∘ g)(x) (g ∘ f)(x)
10/18/2017 HW Sec. 1.6-1
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738224 12/12
15.–/4 pointsLarATRMRP7 1.6.060.
Consider the functions below.
(a) Find each of the following.
f ∘ g =
g ∘ f =
Find the domain of f ∘ g. (Enter your answer using interval notation.)
(b) Use a graphing utility to graph f ∘ g and g ∘ f. Determine whether f ∘ g = g ∘ f.
Yes, they are equal.
No, they are not equal.
f(x) = |x|, g(x) = −x2 + 7
10/18/2017 HW Sec. 1.6-2
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738225 1/9
Current Score : – / 37 Due : Thursday, October 19 2017 10:59 PM EDT
1. –/2 pointsLarATRMRP7 1.6.068.
Use the graphs of f and g to evaluate the functions.
(a) (f − g)(3)
(b) (fg)(3)
2. –/2 pointsLarATRMRP7 1.6.070.MI.
Use the graphs of f and g to evaluate the functions.
(a) (f ∘ g)(3)
(b) (g ∘ f)(1)
HW Sec. 1.6-2 (Homework)
Janean Owens MTH-151, section 90, Fall 2017 Instructor: Mushtaq Khan
WebAssign
10/18/2017 HW Sec. 1.6-2
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738225 2/9
3. –/8 pointsLarATRMRP7 1.6.070.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Use the graphs of f and g to evaluate the functions.
Exercise (a)
Click here to begin! Exercise (b)
Click here to begin!
4. –/1 pointsLarATRMRP7 1.6.090.
Determine whether the statement is true or false.
Given two functions and you can calculate if and only if the range of g is a subset of the domain of f.
True
False
(f ∘ g)(0)
(g ∘ f)(3)
f g, (f ∘ g)(x)
10/18/2017 HW Sec. 1.6-2
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738225 3/9
5. –/5 pointsLarATRMRP7 1.6.501.XP.
Find the following. (Simplify your answers completely.)
What is the domain of f/g? (Enter your answer using interval notation.)
f(x) = 5x − 9, g(x) = 9
(a) (f + g)(x) =
(b) (f − g)(x) =
(c) (fg)(x) =
(d) (f/g)(x) =
10/18/2017 HW Sec. 1.6-2
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738225 4/9
6. –/5 pointsLarATRMRP7 1.6.502.XP.
Find the following. (Simplify your answers completely.)
(a) (f + g)(x) =
(b) (f − g)(x) =
(c) (fg)(x) =
(d) (f/g)(x) =
What is the domain of f/g? (Enter your answer using interval notation.)
7. –/1 pointsLarATRMRP7 1.6.503.XP.
Evaluate the indicated function for and algebraically. If possible, use a graphing utility to verify your answer.
f(x) = , g(x) = x3x x + 8
f(x) = x2 − 4 g(x) = x − 3
(fg)(−2)
10/18/2017 HW Sec. 1.6-2
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738225 5/9
8. –/1 pointsLarATRMRP7 1.6.504.XP.
Evaluate the indicated function for and algebraically. If possible, use a graphing utility to verify your answer.
f(x) = x2 − 1 g(x) = x − 4
(f + g)(t − 4)
10/18/2017 HW Sec. 1.6-2
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738225 6/9
9. –/2 pointsLarATRMRP7 1.6.508.XP.
The annual cost C (in thousands of dollars) and revenue R (in thousands of dollars) for a company each year from 2004 through 2010 can be approximated by the models
where t is the year, with corresponding to 2004.
(a) Write a function P that represents the annual profits of the company. =
(b) Use a graphing utility to graph in the same viewing window.
C = 260 − 8t + 1.5t2 and R = 320 + 2.8t t = 4
P(t)
C, R, and P
10/18/2017 HW Sec. 1.6-2
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738225 7/9
10.–/1 pointsLarATRMRP7 1.6.VE.001.
Watch the video below then answer the question.
True
False
(x) = .f g
f(x) g(x)
10/18/2017 HW Sec. 1.6-2
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738225 8/9
11.–/1 pointsLarATRMRP7 1.6.VE.002.
Watch the video below then answer the question.
Find the composition of two functions
View Transcript
For the following functions, what is the composition (f ∘ g)(x)? f(x) = x + 6 g(x) = 3 x - 3
10/18/2017 HW Sec. 1.6-2
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16738225 9/9
12.–/8 pointsLarATRMRP7 1.6.509.XP.
The suggested retail price of a new car is p dollars. The dealership advertised a factory rebate of $3000 and a 15% discount.
(a) Write a function R in terms of p giving the cost of the car after receiving the rebate from the factory. =
(b) Write a function S in terms of p giving the cost of the car after receiving the dealership discount.
=
(c) Form the composite functions and
=
=
Interpret each composite function.
represents the cost if the rebate is taken before the discount, and represents the cost if the
discount is taken before the rebate.
represents the cost if the rebate is taken before the discount and represents the cost if the
discount is taken before the rebate.
(d) Find and
= $
= $
Which yields the lower cost for the car? Explain.
The discount first yields a lower cost because it is applied to the full amount and then the rebate is taken.
The rebate first yields a lower cost because it is applied to the full amount and then the discount is taken.
R(p)
S(p)
(R ∘ S)(p) (S ∘ R)(p).
(R ∘ S)(p)
(S ∘ R)(p)
(R ∘ S)(p) (S ∘ R)(p)
(S ∘ R)(p) (R ∘ S)(p)
(R ∘ S)(18,400) (S ∘ R)(18,400). (R ∘ S)(18,400) (S ∘ R)(18,400)
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