5-4 Analyzing Graphs Of Polynomial Functions Worksheet With Answers Page 16
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23SOLUTION:
a. Relative maxima: x = – 3.5, x = – 1.75 and x = 1; Relative minima: x = –2.5, x = –1 and x = 2
b. The zeros are at: x = –4, –3, 0, 1.5, and 2.75.
c. Since the graph has 6 turning points, the smallest possible degree of the polynomial function is (6 + 1) or 7.
5-4 Analyzing Graphs of Polynomial Functions
d . Domain: {all real numbers}; Range: {all real numbers};
40. CCSS REASONING The number of subscribers using pagers in the United States can be modeled by
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3
2
f (x) = 0.015x
– 0.44x
+ 3.46x
– 2.7x + 9.68
where x is the number of years after 1990 and f (x) is the number of subscribers in millions.
a. Graph the function.
b. Describe the end behavior of the graph.
c. What does the end behavior suggest about the number of pager subscribers?
d. Will this trend continue indefinitely? Explain your reasoning.
SOLUTION:
a. Use a graphing calculator to graph the function.
b. As x increases, f (x) increases.
c. Sample answer: The graph suggests that the number of pager subscribers will increase dramatically and continue
to increase.
d . Sample answer: The graph is unreasonable for
since pager use is currently decreasing rapidly and pagers
have been replaced by more efficient products.
For each function,
a. determine the zeros, x- and y-intercepts, and turning points,
b. determine the axis of symmetry, and
c. determine the intervals for which it is increasing, decreasing, or constant.
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2
42. f (x) = x
– 8x
+ 16
SOLUTION:
Graph the function.
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