Questions: Analyze the polynomial function f(x)=(x+5)^2(1-x) using parts (a) through (h) below. (e) Approximate the turning points of the graph. The turning point(s) of the graph is/are (-5,0),(-1,32). (Type an ordered pair. Round each coordinate to the nearest hundredth as needed. Use a comma to separate answers as needed.) (f) Use the information in parts (a) through (e) to draw a complete graph of the function by hand. Choose the correct graph below. A. B. C. D. (g) From the graph, find the range of the polynomial function. The range of the polynomial function f is (-∞, ∞). (Type your answer in interval notation. Round to the nearest hundredth as needed.) (h) Use the graph to determine where the function is increasing and where it is decreasing. The function is increasing on the interval(s) . (Type your answer in interval notation. Round to the nearest hundredth as needed. Use a comma to separate answers as needed.)

Analyze the polynomial function f(x)=(x+5)^2(1-x) using parts (a) through (h) below. (e) Approximate the turning points of the graph. The turning point(s) of the graph is/are (-5,0),(-1,32). (Type an ordered pair. Round each coordinate to the nearest hundredth as needed. Use a comma to separate answers as needed.) (f) Use the information in parts (a) through (e) to draw a complete graph of the function by hand. Choose the correct graph below. A. B. C. D. (g) From the graph, find the range of the polynomial function. The range of the polynomial function f is (-∞, ∞). (Type your answer in interval notation. Round to the nearest hundredth as needed.) (h) Use the graph to determine where the function is increasing and where it is decreasing. The function is increasing on the interval(s) . (Type your answer in interval notation. Round to the nearest hundredth as needed. Use a comma to separate answers as needed.)
Transcript text: Analyze the polynomial function $f(x)=(x+5)^{2}(1-x)$ using parts (a) through (h) below. (e) Approximate the turning points of the graph. The turning point(s) of the graph is/are $(-5,0),(-1,32)$. (Type an ordered pair. Round each coordinate to the nearest hundredth as needed. Use a comma to separate answers as needed.) (f) Use the information in parts (a) through (e) to draw a complete graph of the function by hand. Choose the correct graph below. A. B. C. D. (g) From the graph, find the range of the polynomial function. The range of the polynomial function $f$ is $\square$ $(-\infty, \infty)$. (Type your answer in interval notation. Round to the nearest hundredth as needed.) (h) Use the graph to determine where the function is increasing and where it is decreasing. The function is increasing on the interval(s) $\square$ $\square$. (Type your answer in interval notation. Round to the nearest hundredth as needed. Use a comma to separate answers as needed.)
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Solution

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Step 1: Identify the turning points.

The turning points are given as (-5, 0) and (-1, 32).

Step 2: Choose the correct graph.

The correct graph is B because it displays the given turning points and the correct end behavior for a negative cubic function (upward to the left, downward to the right).

Step 3: Determine the range.

The graph extends infinitely downwards and upwards. Therefore, the range is (-∞, ∞).

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