Power FunctionsDef. A power function is of the form where k and p are constant.

• Exponential functions dominate power functions as x.

Ex.

py k x

2

2lim

x

x x

Ex. How many times do y = 2x and y = x2 intersect?

Remember that

Ex.4

38

mn

mna a

Inverse FunctionsDef. A function is invertible if no two points

have the same y-coordinate.

• Each y corresponds to at most one x

• The graph passes the horizontal line test

• To find the inverse, switch x and y, and then solve for y.

You may not find the equation for the inverse, even if the function is invertible

Ex. Let , find 1

2 5f x

x

1f x

Ex. Sketch 1f x

2

-2

Domain of f Range of f -1

Range of f Domain of f -1

(distance as a function of time) d = f (t)

becomes

(time as a function of distance) t = f -1(d)

Ex. Let C = f (q) be the cost, in dollars, for Dunder Mifflin to produce q boxes of paper. Using correct units, explain the meaning of f -1(25) = 1000.

Ex. Suppose D = f (A) is the cost, in dollars, for Apu to build a Kwik-E-Mart with area A ft.2 Using correct units, explain the meaning of:

a) f (10,000)

b) f -1(20,000)