Questions: Question 9 of 13 This quiz: 13 point(s) possible This question: 1 point(s) possible The comprehensive graphs of four polynomial functions are shown in A-D. [Four graphs of polynomial functions labeled A, B, C, and D are shown] Which of the graphs cannot be that of a cubic polynomial function? The graph(s) in [ ] cannot be the graph of a cubic polynomial function. (Type A, B, C, or D. Use commas to separate answers as needed.)

Question 9 of 13

This quiz: 13 point(s) possible
This question: 1 point(s) possible

The comprehensive graphs of four polynomial functions are shown in A-D.

[Four graphs of polynomial functions labeled A, B, C, and D are shown]

Which of the graphs cannot be that of a cubic polynomial function?

The graph(s) in [ ] cannot be the graph of a cubic polynomial function.
(Type A, B, C, or D. Use commas to separate answers as needed.)

Transcript text: Question 9 of 13 This quiz: 13 point(s) possible This question: 1 point(s) possible The comprehensive graphs of four polynomial functions are shown in A-D. [Four graphs of polynomial functions labeled A, B, C, and D are shown] Which of the graphs cannot be that of a cubic polynomial function? The graph(s) in [ ] cannot be the graph of a cubic polynomial function. (Type A, B, C, or D. Use commas to separate answers as needed.)

Solution

Solution Steps

Step 1: Analyze the question

The question asks which graphs cannot be that of a cubic polynomial function. Cubic functions have a degree of 3, meaning the highest power of x is 3.

Step 2: Analyze Graph A

Graph A has 3 turning points. The maximum number of turning points for a polynomial of degree _n_ is _n_-1. Hence, Graph A must be at least a quartic function (degree 4). Thus, it cannot be a cubic function.

Step 3: Analyze Graph B

Graph B has 2 turning points. This means it can be a cubic function.

Step 4: Analyze Graph C

Graph C has one turning point. Technically, this could be a cubic function that doesn't make full use of its possible turning points. So, it can be a cubic.

Step 5: Analyze Graph D

Graph D has two turning points. Like B, this can be a cubic function.