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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)