Question 1

Which of the following is a characteristic of the graph of any polynomial function of degree 2 or higher?

Accepted Answer

It is smooth and continuous, with only rounded curves and no breaks.

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

If $$f(x) = 3(x-1)^2$(x+2)$$, what is the degree of the polynomial and what is its end behavior?

Accepted Answer

Degree 3, falls left and rises right

Question 5

Which of the following statements about the zeros of a polynomial function is TRUE?

Accepted Answer

Each zero of even multiplicity causes the graph to touch the x-axis and turn around.

Question 6

Suppose $$f(x) = -4x^2$(x-1)^3(x+5$$)$$. What is the degree of f(x$$)$ and what is the end behavior?

Accepted Answer

Degree 6, falls left and right

Question 7

A real-world model for the number of new AIDS cases in the U.S. is given by $$f(x) = -49x^3$ + 806x^2$ + 3776x + 2503$$, where $$x is $$years after 1983. According to the Leading Coefficient Test, what does the end behavior of this model suggest about its long-term appropriateness?

Accepted Answer

The model predicts the number of cases will fall without bound, which is not realistic for long-term predictions.

Question 8

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

Accepted Answer

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

Question 9

Which of the following best describes the maximum number of turning points for a polynomial function of degree $$n$$?

Accepted Answer

$$n-1$$

Question 10

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

Accepted Answer

$$-24$$

Question 11

If $$f(x) = (x+1)^2$(x-3)^3$$, which statement about the graph at $$x = -1$$ and $$x = 3$ is correct?

Accepted Answer

The graph touches and turns at $$x = -1$$ and crosses at $$x = 3.$$

Question 12

Which of the following is NOT a property of polynomial functions?

Accepted Answer

They can have vertical asymptotes.

Question 13

Suppose $$f(x) is a $$polynomial function with $$f(-2) = 5$$ and $$f(-3) = -42. $$What does the Intermediate Value Theorem guarantee?

Accepted Answer

There is a zero of $$f(x)$$ between $$x = -2$$ and $$x = -3.$$

Question 14

If $$f(x) = x^3$ - 2x^2$ - 8x$$, what are the zeros and their multiplicities?

Accepted Answer

$$x = 0 ($$multiplicity 1), $$x = 2 ($$multiplicity 1), $$x = -4 ($$multiplicity 1)

Question 15

Which of the following is true about the symmetry of polynomial functions?

Accepted Answer

A polynomial function is symmetric about the y-axis if $$f(-x) = f(x).$$

Question 16

A polynomial function $$f(x)$$ has degree 4 and a negative leading coefficient. What is the end behavior of its graph?

Accepted Answer

Falls left, falls right

Question 17

If $$f(x) = (x-2)^2$(x+1)$$, which of the following statements is correct?

Accepted Answer

The graph crosses the x-axis at $$x = -1$$ and touches at $$x = 2.$$

Polynomial Functions and Their Graphs: Study Notes for College Algebra

Study Guide - Practice Questions

Study Guide - Flashcards