Graph each function by fi nding the x- and y-intercepts and one other point. 79) g(x) 3x 3 80) k(x) 2x 6 81) f (x) 1 2 x 2 82) f (x) 1 3 x 1 83) h(x) x 84) f (x) x Graph each function using the slope and y-intercept. 85) f (x) 4x 1 86) f (x) x 5 87) g(x) 1 4 x 2 88) h(x) 3 5 x 2 89) g(x) 2x 1 2 90) h(x) 3x 1 Graph each function 91) s(t) 1 3 t 2 92) k(d ) d 1 93) A(r) 3r 94) N(t) 3.5t 1 Objective 7: Solve Problems Using Linear Functions 95) A truck on the highway travels at a constant speed of 54 mph. The distance, D (in miles), that the truck travels after t hr can be defi ned by the function D(t) 54t a) How far will the truck travel after 2 hr? b) How far will the truck travel after 4 hr? c) How long does it take the truck to travel 135 mi? d) Graph the function. 96) The velocity of an object, v (in feet per second), of an object during free-fall t sec after being dropped can be defi ned by the function v(t) 32t a) Find the velocity of an object 1 sec after being dropped. b) Find the velocity of an object 3 sec after being dropped. c) When will the object be traveling at 256 ft/sec? d) Graph the function. 65) f (x) 3x 2. Find x so that f (x) 10. 66) f (x) 5x 4. Find x so that f (x) 9. 67) g(x) 2 3 x 1. Find x so that g(x) 5. 68) h(x) 1 2 x 6. Find x so that h(x) 2. Objective 5: Evaluate a Function for Variables or Expressions Fill It In Fill in the blanks with either the missing mathematical step or reason for the given step. 69) Let f (x) 9x 2. Find f (n 3). Substitute n 3 for x. 9n 27 2 Simplify. 70) Let f (x) 4x 5. Find f (k 6). f (k 6) 4(k 6) 5 Distribute. Simplify. 71) f (x) 7x 2 and g(x) x2 5x 12. Find each of the following, and simplify. a) f (c) b) f (t) c) f (a 4) d) f (z 9) e) g(k) f ) g(m) g) f (x h) h) f (x h) f (x) 72) f (x) 5x 6 and g(x) x2 3x 11. Find each of the following, and simplify. a) f (n) b) f (p) c) f (w 8) d) f (r 7) e) g(b) f) g(s) g) f (x h) h) f (x h) f (x) Objective 6: Define and Graph a Linear Function Graph each function by making a table of values and plotting points. 73) f (x) x 4 74) f (x) x 2 75) f (x) 2 3 x 2 76) g(x) 3 5 x 2 77) h(x) 3 78) g(x) 1 www.mhhe.com/messersmith SECTION 4.5 Introduction to Functions 211
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