College Algebra 9th txtbk

186 CHAPTER 3 FUNCTIONS
In Problems 59–64, use the graph of f to find a piecewise
definition for f.
59.
f(x)
64.
f(x)
5
(2, 4)
(4, 4)
5
(2, 3)
5
(0, 1)
(0, 1)
5
(2, 3)
x
5
(3, 1)
(4, 3)
(3, 3)
5
(2, 0)
5
x
60.
61.
62.
63.
5
(2, 2)
5
(4, 3) (1, 3)
5
5
(4, 3) (2, 3)
(2, 2)
5
5
5
5
(0, 2)
5
f(x)
5
f(x)
5
5
(4, 2)
(2, 2)
(0, 2)
5
f(x)
f(x)
(2, 2)
5
(1, 3)
(4, 1)
x
5
(1, 1) (4, 1)
(1, 4)
5
x
5
x
x
In Problems 65–68, find a piecewise definition of f that does not
involve the absolute value function. (Hint: Use the definition of
absolute value on page 180 to consider cases.) Sketch the graph of
f, and find the domain, range, and the values of x at which f is
discontinuous.
65. f (x) 1 x 66. f (x) 2 x
67. f (x) x 2 68. f (x) x 1
69. The function f is continuous and increasing on the interval
[1, 9] with f(1) 5 and f(9) 4.
(A) Sketch a graph of f that is consistent with the given
information.
(B) How many times does your graph cross the x axis? Could the
graph cross more times? Fewer times? Support your conclusions
with additional sketches and/or verbal arguments.
70. Repeat Problem 69 if the function is not continuous.
71. The function f is continuous on the interval [5, 5] with
f(5) 4, f(1) 3, and f(5) 2.
(A) Sketch a graph of f that is consistent with the given
information.
(B) How many times does your graph cross the x axis? Could the
graph cross more times? Fewer times? Support your conclusions
with additional sketches and/or verbal arguments.
72. Repeat Problem 71 if f is continuous on [8, 8] with
f(8) 6, f(4) 3, f(3) 2, and f(8) 5.
Problems 73–80 require the use of a graphing calculator.
In Problems 73–78, first graph functions f and g in the same
viewing window, then graph m(x) and n(x) in their own viewing
windows:
m(x) 0.5[ f (x) g(x) f (x) g(x)]
n(x) 0.5[ f (x) g(x) f (x) g(x)]
73. f(x) 2x, g(x) 0.5x
74. f(x) 3x 1, g(x) 0.5x 4
75. f(x) 5 0.2x 2 , g(x) 0.3x 2 4
76. f(x) 0.15x 2 5, g(x) 5 1.5x
77. f(x) 0.2x 2 0.4x 5, g(x) 0.3x 3
78. f(x) 8 1.5x 0.4x 2 , g(x) 0.2x 5
79. How would you characterize the relationship between f, g, and
m in Problems 73–78? [Hint: Use the trace feature on the calculator
and the up/down arrows to examine all 3 graphs at several
points.]