Determine which viewing rectangle produces the most appropriate graph of the function. $g ( x ) = 6 x ^ { 3 } - 15 x ^ { 2 } + 4 x - 1$
A) $[ - 2,2 ] \text { by } [ - 2,2 ]$
B) $[ - 8,8 ] \text { by } [ - 8,8 ]$
C) $[ - 4,4 ] \text { by } [ - 12,12 ]$
D) $[ - 100,100 ] \text { by } [ - 100,100 ]$
E) $[ - 10,10 ] \text { by } [ - 100,100 ]$

Question

Quizplus · Accepted Answer

To graph the function, we need to determine a viewing rectangle that captures the behavior of the function. Since the leading term is $6x^3$ and the coefficient is positive, we know that the end behavior of the graph as $x 	o \pm \infty$ will be that the graph will rise on the right and fall on the left. Hence, we need to choose a viewing window wide enough to show this behavior.

Choices A and B are too narrow, they only span 4 or 8 units on the $x$-axis, respectively. So, we are left to consider only choices C, D, and E.

Choice D is too wide, spanning 200 units on the $x$-axis, and will make the graph too small to read any features.

Choice E is reasonable in width, but spanning 200 units on the $y$-axis is not necessary, as the function only ranges from $-\infty$ to $\infty$.

So, the best choice is choice C, which has a reasonable width on the $x$-axis to capture the end behavior, and extends far enough on the $y$-axis to show any interesting features.

Determine Which Viewing Rectangle Produces the Most Appropriate Graph of the Function