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Power Functions Def. A power function is of the form where k and p are constant. Exponential functions dominate power functions as x. Ex.

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

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Inverse Functions Def. 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

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Ex. Let, find

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Ex. Sketch

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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)

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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.

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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)

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3.2 Inverse Functions and Logarithms 3.3 Derivatives of Logarithmic and Exponential functions.

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