Determine a viewing window that will provide a complete graph of the function.
-$$y = 3 x ^ { 3 } - 26 x ^ { 2 } + 18 x - 47$$
A) $[ - 3,10 ]$ by $[ - 400,100 ]$
B) $[ - 10,10 ]$ by $[ - 150,150 ]$
C) $[ - 8,10 ]$ by $[ - 100,300 ]$
D) $[ - 5,5 ]$ by $[ - 500,100 ]$

Question

Quizplus · Accepted Answer

To determine a suitable viewing window for the given cubic function, we need to consider the behavior of the function at its critical points and its end behavior. The critical points, where the derivative equals zero or is undefined, give us information about the local maxima and minima of the function. For cubic functions, the end behavior is such that as $x$ approaches infinity, the function will go towards infinity or negative infinity depending on the leading coefficient. Given the coefficients and the degree of the polynomial, a window of $[-3,10]$ by $[-400,100]$ is wide and tall enough to capture the significant features of the function, including its turning points and intercepts, without being excessively large. Other options either do not provide a wide enough range to capture the full behavior of the function or do not offer a suitable vertical range to include all critical points and the overall shape of the graph.

Determine a Viewing Window That Will Provide a Complete Graph y=3x3−26x2+18x−47y = 3 x ^ { 3 } - 26 x ^ { 2 } + 18 x - 47y=3x3−26x2+18x−47

Determine a Viewing Window That Will Provide a Complete Graph $y = 3 x ^ { 3 } - 26 x ^ { 2 } + 18 x - 47$