SECTION 2.2 The Graph of a Function 85 40. Challenge Problem Suppose f x x x c 4 2 ( ) = − + and g x f x 3 4. ( ) ( ) = − Find f 3( ) if g 2 5. ( ) − = 41. Challenge Problem Suppose f x x 2 ( ) = + and g x x n. 2 ( ) = + If f g 5 4, ( ) ( ) = what is the value of g n ? ( ) 39. Reading and Interpreting Graphs Let C be the function whose graph is given below. This graph represents the cost C of using g gigabytes of data in a month for a data-only plan. (a) Find C 0 . ( ) Interpret this value. (b) Find C 5 . ( ) Interpret this value. (c) Find C 15 . ( ) Interpret this value. (d) What is the domain of C? What does this domain imply in terms of the number of gigabytes? (e) Describe the shape of the graph. C g (0, 50) 0 10 20 30 100 200 300 Cost (dollars) Gigabytes (5, 50) (15, 150) (30, 300) Explaining Concepts 42. Describe how you would find the domain and range of a function if you were given its graph. How would your strategy change if you were given the equation defining the function instead of its graph? 43. How many x-intercepts can the graph of a function have? How many y-intercepts can the graph of a function have? Explain why. 44. Is a graph that consists of a single point the graph of a function? Can you write the equation of such a function? 45. Match each of the following functions with the graph that best describes the situation. (a) The cost of building a house as a function of its square footage (b) The height of an egg dropped from a 300-foot building as a function of time (c) The height of a human as a function of time (d) The demand for Big Macs as a function of price (e) The height of a child on a swing as a function of time (I) x (II) (III) x (IV) x (V) x y y y y y x 46. Match each of the following functions with the graph that best describes the situation. (a) The temperature of a bowl of soup as a function of time (b) The number of hours of daylight per day over a 2-year period (c) The population of Florida as a function of time (d) The distance traveled by a car going at a constant velocity as a function of time (e) The height of a golf ball hit with a 7-iron as a function of time (I) (II) (III) (IV) (V) x y x y x y x y x y
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