Polymomials
Linear Functions-----y=mx+b
F(x)=2x+1
Y=1, m=0
G(x)=-2x+1
M<0
Decreasing
x=2
slope is undefined
(2,0)
Quadratic functions, y=ax^2+bx+c
y=x^2
f(x)=x^2+2
Y=-x^2
H(x)=(x+2)^2=x^2+4x+4
Y=x^3
Y=√x, x≥0
Y=3√x
(1,1)
1/x, x≠0
--------------------------------------------------going over past------------------------------------------
y-y_1=m(x-x_1)
Chapter R functions, Gtaphs, and Models
(R.4) Slope & Linear Functions
Ex) Find the equation of the line through (-2, 4) with slope m= -3/5
Y-4=-3/5(x-(-2))
y-4= -3/5(x+2)
y=-3/5(x+2)+4
y=(-3/5)x-6/5+4
y=(-3/5)x+14/5
ex) write the equation of the line through (-2, 4) and (1,2) m= 4-2/-2-1 =2/-3
y-2=-2/3(x-1)
y=-2/3(x-1)+2
y=(-2/3)x+2/3+2
y=(-2/3)x+8/3
ex) The management of a firm producing poultry feed plants to charge $24 per bag. The cost has a fixed component of $100, and increases by $20 per bag produced.
(a) Find the revenue function: R(x)=(price)x<price per unit>
R(x)=24x
(b) Find the cost function: C(x)=20x+100<x units produced & sold>
(c) How many units must be produced and sold for the firm to break even(가격=레비뉴)?
R(x)=C(x)
24=20x+100
4x=100
X=25 units
(d) What is the common dollar value for the break even cost and revenue?
R(25)=24(25)=$600
C(x)=20x+100
600
100
25
R(x)=24x
(e) Use the cost and revenue to determine the profit function for X units produced & sold.
P(x)=R(X)-C(x)
=24x-(20x+100)
=24x-20x-100
P(x)=4x-100
(f) What is the profit if 50 units are produced and sold?
P(50)=4(50)-100=$100 p(x)=4x-100
(
-100
)

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