Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate
graph of the specified function.
-$$f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 3 x + 20$$
A) $[ - 2,2 ]$ by $[ - 10,10 ]$
B) $[ - 5,5 ]$ by $[ - 5,25 ]$
C) $[ - 5,25 ]$ by $[ - 5,5 ]$
D) $[ - 20,20 ]$ by $[ - 100,100 ]$

Question

Quizplus · Accepted Answer

Using a graphing calculator or computer to graph the function, we can see that the shape of the graph is a "hill" that peaks at around $x = 1$ and then slopes downward. The $y$-intercept is $y=20$.

Choices A and D have too wide of a horizontal range, which causes the graph to appear too stretched out horizontally. Choice C has the horizontal and vertical ranges switched, which makes the graph appear very elongated and difficult to read.

Choice B has a good balance between horizontal and vertical ranges. The vertical range is sufficient to show the full shape of the graph and the horizontal range is not too wide, allowing for a clearer visualization of concavity and key points of the function. Therefore, choice B is the best option.

Use a Graphing Calculator or Computer to Determine Which of the Given