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 )