Question 1

Which of the following is a polynomial function?

Accepted Answer

$f(x) = x^3 - 4x + 7$

Question 2

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

Accepted Answer

Rises to the left and falls to the right

Question 3

Which statement best describes the graph of a polynomial function of degree 2 or higher?

Accepted Answer

It is smooth and continuous.

Question 4

If $f(x) = (x - 2)^3(x + 1)^2$, what are the zeros and their multiplicities?

Accepted Answer

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

Question 5

A zero of a polynomial function has even multiplicity. What does the graph do at this zero?

Accepted Answer

It touches the x-axis and turns around.

Question 6

Use the Intermediate Value Theorem to determine if $f(x) = x^3 - 4x + 1$ has a real zero between $x = 1$ and $x = 2$.

Accepted Answer

Yes, because $f(1)$ and $f(2)$ have opposite signs.

Question 7

What is the maximum number of turning points for a polynomial function of degree $n$?

Accepted Answer

$n - 1$

Question 8

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

Accepted Answer

$-24$

Question 9

Which of the following functions is symmetric about the y-axis?

Accepted Answer

$f(x) = x^2 + 4$

Question 10

If $f(x) = x^4 - 2x^2 + 1$, what is the degree and leading coefficient?

Accepted Answer

Degree 4, leading coefficient 1

Question 11

A chemical reaction rate is modeled by $R(t) = -t^3 + 6t^2 - 9t + 2$. What is the end behavior of $R(t)$ as $t$ increases without bound?

Accepted Answer

Falls to the right

Question 12

Which of the following is NOT a characteristic of the graph of a polynomial function?

Accepted Answer

It has sharp corners.

Question 13

If $f(x) = (x - 1)^4(x + 2)$, how does the graph behave at $x = 1$?

Accepted Answer

It touches the x-axis and turns around.

Question 14

A medical dosage model is given by $D(x) = 5x^2 - 20x + 15$. What is the degree and leading coefficient?

Accepted Answer

Degree 2, leading coefficient 5

Question 15

If $f(x) = -x^6 + 3x^2 - 2$, what is the end behavior of the graph?

Accepted Answer

Falls to both left and right

Question 16

Which of the following is true about the zeros of $f(x) = (x - 4)^2(x + 1)^3$?

Accepted Answer

At $x = 4$, the graph touches the x-axis and turns around.

Question 17

A polynomial function $f(x)$ has degree 5 and a negative leading coefficient. What is the end behavior?

Accepted Answer

Falls to the left and rises to the right

Question 18

If $f(x) = x^3 - 6x^2 + 11x - 6$, which value is a zero of $f(x)$?

Accepted Answer

$x = 1$

Question 19

A polynomial $f(x)$ has a zero at $x = 5$ with multiplicity 3. What does the graph do at $x = 5$?

Accepted Answer

Crosses the x-axis and flattens out

Question 20

Which of the following is a correct application of the Intermediate Value Theorem?

Accepted Answer

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

Chapter 3: Polynomial Functions and Their Graphs – College Algebra Study Notes

Study Guide - Practice Questions