19. In parts (a) to (f), use the following graph. x y –7 7 7 –7 (2, –6) (0, –3) (–3, 5) (a) Find the intercepts. (b) Based on the graph, tell whether the graph is symmetric with respect to the x-axis, the y-axis, and/or the origin. (c) Based on the graph, tell whether the function is even, odd, or neither. (d) List the intervals on which f is increasing. List the intervals on which f is decreasing. (e) List the numbers, if any, at which f has a local maximum. What are the local maximum values? (f) List the numbers, if any, at which f has a local minimum. What are the local minimum values? 20. Determine algebraically whether the function ( ) = − f x x x 5 9 2 is even, odd, or neither. 21. For the function f x x x x x 2 1 if 3 2 3 4 if 2 ( ) = + − < < − + ≥ ⎧ ⎨ ⎪⎪ ⎩⎪⎪ (a) Find the domain of f. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. 22. Graph the function ( ) ( ) = − + + f x x 3 1 5 2 using transformations. 23. Suppose that ( ) = − + f x x x5 1 2 and ( ) = − − g x x4 7. (a) Find + f g and state its domain. (b) Find f g and state its domain. 24. Demand Equation The price p (in dollars) and the quantity x sold of a certain product obey the demand equation = − + ≤ ≤ p x x 1 10 150, 0 1500 (a) Express the revenue R as a function of x. (b) What is the revenue if 100 units are sold? (c) What quantity x maximizes revenue? What is the maximum revenue? (d) What price should the company charge to maximize revenue? 270 CHAPTER 4 Polynomial and Rational Functions
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