Question 1

Which of the following is NOT a characteristic of the graph of a polynomial function of degree 2 or higher?

Accepted Answer

The graph can have breaks or holes.

Question 2

Given the polynomial function $$f(x) = -2x^5$ + 3x^3$ - x + 7$$, use the Leading Coefficient Test to determine its end behavior.

Accepted Answer

Rises left, falls right

Question 3

A polynomial function $$f(x)$$ has a zero at $$x = 4$$ with multiplicity 3. Which statement best describes the behavior of the graph at $$x = 4$$?

Accepted Answer

The graph crosses the x-axis at $$x = 4$$ and flattens out near the intercept.

Question 4

Which of the following polynomial functions has the same end behavior on both sides?

Accepted Answer

$$f(x) = -x^4$ + 5x^2$ - 3$$

Question 5

Suppose $$f(x) = (x - 1)^2$(x + 3). $$What are the zeros and their multiplicities?

Accepted Answer

$$x = 1 ($$multiplicity 2), $$x = -3 ($$multiplicity 1)

Question 6

A real-world model for the number of new AIDS cases in the U.S. is $$f(x) = -49x^3$ + 806x^2$ + 3776x + 2503$$, where $$x is $$years after 1983. Why is this model only appropriate for a limited time period?

Accepted Answer

Because the graph eventually falls without bound, predicting negative cases, which is impossible.

Question 7

If $$f(x) = x^4$ - 4x^2$, what are the x$-intercepts of the graph?

Accepted Answer

$$x = 0$$, $$x = 2$$, and $$x = -2$$

Question 8

Which of the following statements about the Intermediate Value Theorem is correct?

Accepted Answer

If $$f(a)$$ and $$f(b)$$ have opposite signs, there is at least one zero between $$a$$ and $$b.$$

Question 9

Given $$f(x) = 2(x + 2)^2$(x - 3)$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$y = -24$$

Question 10

A polynomial function $$f(x)$$ has degree 6. What is the maximum number of turning points its graph can have?

Accepted Answer

5

Question 11

Which of the following functions is an example of a polynomial function?

Accepted Answer

$$f(x) = x^2$ + 3x - 5$$

Question 12

If $$f(x) = -4x^3$(x - 1)^2$(x + 5)$$, what is the end behavior of the graph?

Accepted Answer

Falls left, falls right

Question 13

Suppose $$f(x) = (x - 2)^4$(x + 1). $$How does the graph behave at $$x = -1$$?

Accepted Answer

The graph crosses the x-axis.

Question 14

Which of the following best describes the symmetry of $$f(x) = x^4$?

Accepted Answer

Y-axis symmetry

Question 15

If $$f(x) = x^3$ - 2x - 5$$, use the Intermediate Value Theorem to determine if there is a real zero between $$x = 2$$ and $$x = 3.$$

Accepted Answer

Yes, because $$f(2)$$ and $$f(3)$$ have opposite signs.

Question 16

Which of the following is true about the zeros of a polynomial function?

Accepted Answer

Each real zero corresponds to an x-intercept.

Polynomial Functions and Their Graphs: College Algebra Study Guide

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