Q: Which of the following best describes the end behavior of the polynomial function shown in the graph?

As $$x \to -\infty$$, $$f(x) \to -\infty$$ and as $$x \to \infty$$, $$f(x) \to \infty$$

Question 1

Which of the following best describes the end behavior of the polynomial function shown in the graph?

Accepted Answer

As $$x 	o -\infty$$, $$f(x) 	o -\infty$$ and as $$x 	o \infty$$, $$f(x) 	o \infty$$

Question 2

Based on the graph, what is the minimum possible degree of the polynomial function?

Accepted Answer

3

Question 3

How many turning points does the graph of the polynomial function have?

Accepted Answer

2

Question 4

Which of the following statements about the zeros of the polynomial function is correct based on the graph?

Accepted Answer

The function has three real zeros.

Question 5

At which x-value does the graph appear to touch the x-axis and turn around, indicating a zero of even multiplicity?

Accepted Answer

$$x = -2$$

Question 6

If the leading coefficient of the polynomial function is positive, what can you conclude about the end behavior?

Accepted Answer

The right end rises and the left end falls.

Question 7

Suppose the polynomial function represented by the graph is $$f(x) = 2x^3$ + bx^2$ + cx + d. $$Which feature of the graph confirms that the degree is odd?

Accepted Answer

The ends of the graph go in opposite directions.

Question 8

If the graph crosses the x-axis at $$x = 1$$, what does this indicate about the zero at $$x = 1$$?

Accepted Answer

It is a zero of odd multiplicity.

Question 9

Given the graph, which of the following could be the factored form of the polynomial function?

Accepted Answer

$$f(x) = 2(x + 2)^2$(x - 1)$$

Question 10

If the y-intercept of the graph is $$-8$$, what is the value of $$f(0)$$?

Accepted Answer

$$-8$$

Polynomial Functions: Structure, Zeros, and Graphs

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