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.

Question 2

Given the polynomial function $$f(x) = -2x^5$ + 3x^3$ - x + 7$$, what is the end behavior of its graph?

Accepted Answer

Rises to the left and falls to the right

Question 3

If a polynomial function $$f(x)$$ has a zero at $$x = 4$$ with multiplicity 3, what does the graph do at $$x = 4$$?

Accepted Answer

Crosses the x-axis and flattens out

Question 4

Which of the following polynomial functions has the same end behavior as $$f(x) = 5x^4$ - 2x^2$ + 1$$?

Accepted Answer

$$g(x) = 2x^6$ - x^2$ + 4$$

Question 5

A real-world model for the number of new cases of a disease is given by $$f(x) = -49x^3$ + 806x^2$ + 3776x + 2503$$, where $$x is $$years after 1983. What does the end behavior of this function suggest about the model's long-term validity?

Accepted Answer

The number of cases will eventually become negative, which is not possible.

Question 6

Given $$f(x) = (x + 1)^2$(x - 3)$$, which statement about its zeros and their multiplicities is correct?

Accepted Answer

$$x = -1 is a $$zero of multiplicity 2, and $$x = 3 is a $$zero of multiplicity 1.

Question 7

If $$f(x) = x^4$ - 4x^2$, how many turning points can its graph have at most?

Accepted Answer

3

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

Degree 6, falls left and falls right

Question 10

A polynomial function $$f(x)$$ has $$f(-2) = 5$$ and $$f(-3) = -42. $$What can you conclude using the Intermediate Value Theorem?

Accepted Answer

There is a root between $$x = -2$$ and $$x = -3.$$

Question 11

Which of the following is NOT a step in the five-step strategy for graphing a polynomial function?

Accepted Answer

Find the minimum value of the function.

Question 12

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

Accepted Answer

$$-24$$

Question 13

Which of the following best describes the end behavior of $$f(x) = 7x^6$ - 2x^3$ + 5$$?

Accepted Answer

Rises to the left and rises to the right

Question 14

A polynomial function $$f(x)$$ has a zero at $$x = 1$$ with multiplicity 2 and a zero at $$x = -3$$ with multiplicity 1. Which statement is true?

Accepted Answer

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

Question 15

If $$f(x) is a $$polynomial of degree $$n$$, what is the maximum number of turning points its graph can have?

Accepted Answer

$$n-1$$

Question 16

Which of the following is a necessary condition for a function to be classified as a polynomial function?

Accepted Answer

All exponents of the variable are non-negative integers.

Polynomial Functions and Their Graphs: Study Notes for College Algebra

Study Guide - Practice Questions

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