Free Practice Quiz Question List

02 Polynomial and Rational Functions Online Quiz Questions

Use this free practice quiz with 20 questions to review 02 Polynomial and Rational Functions, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

For the linear function $f(x)=3x-6$ , which value is its zero?

A
$x=-2$
B
$x=0$
C
$x=2$
D
$x=6$

Choose one

1 point

How many real zeros does the quadratic equation $x^2-6x+9=0$ have?

A
Two distinct real zeros
B
One repeated real zero
C
No real zeros and two complex zeros
D
Infinitely many real zeros

Choose one

1 point

What is the horizontal asymptote of $f(x)=\frac{3x^2+1}{x^3-4}$ ?

A
$y=1$
B
$y=0$
C
$x=0$
D
There is a slant asymptote

Choose all

1 point

Select all statements that correctly describe the end behavior of $f(x)=2x^5-x+1$ .

A
As $x\to-\infty$ , $f(x)\to-\infty$
B
As $x\to-\infty$ , $f(x)\to\infty$
C
As $x\to\infty$ , $f(x)\to\infty$
D
As $x\to\infty$ , $f(x)\to-\infty$

Choose all

1 point

Which statements are valid consequences of the Factor Theorem and the Rational Zero Theorem? Select all that apply.

A
If $f(2)=0$ , then $x-2$ is a factor.
B
Every zero of a polynomial with integer coefficients must be an integer.
C
A rational zero must have a numerator dividing the constant term.
D
A polynomial can have a vertical asymptote.

True or false

1 point

Every polynomial function is defined for every real number and therefore has no vertical asymptotes.

A
True
B
False

True or false

1 point

A common factor that cancels between the numerator and denominator of a rational function produces a vertical asymptote.

A
True
B
False

Written response

1 point

Solve $\frac{2}{x-1}=\frac{3}{x+2}$ . Enter the permitted solution value.

Fill in the blank

1 point

In a polynomial, the coefficient of the term with the highest exponent is the , and the highest exponent itself is the .

Fill in the blank

1 point

For $f(x)=\frac{(x-2)(x+1)}{(x-2)(x-3)}$ , the canceled factor creates a at $x=2$ .

Choose one

1 point

Which pair of asymptotes belongs to $h(x)=\frac{x^2+1}{x-1}$ ?

A
The slant asymptote is $y=x+1$ , and the vertical asymptote is $x=1$ .
B
The slant asymptote is $y=x-1$ , and the vertical asymptote is $x=-1$ .
C
The horizontal asymptote is $y=1$ , and there is no vertical asymptote.
D
The horizontal asymptote is $y=0$ , and the vertical asymptote is $x=1$ .

True or false

1 point

True or false: Every polynomial function is defined for every real number.

A
True
B
False

Choose one

1 point

Which number could be a rational zero of $f(x)=6x^3-7x^2+4x+5$ according to the Rational Zero Theorem?

A
$\frac{1}{5}$
B
$\frac{5}{6}$
C
$\frac{3}{5}$
D
$\frac{6}{5}$

Choose one

1 point

What is the $x$ -intercept of the linear function $f(x)=2x-8$ ?

A
$(0,-8)$
B
$(-4,0)$
C
$(4,0)$
D
$(0,4)$

Choose one

1 point

How many real zeros does $f(x)=x^2-6x+9$ have?

A
One repeated real zero
B
Two distinct real zeros
C
No real zeros and two complex zeros
D
Infinitely many real zeros

Choose one

1 point

For $f(x)=(x-3)^2(x+1)$ , how does the graph behave at its real zeros?

A
The graph crosses at $x=3$ and touches at $x=-1$ .
B
The graph touches at both zeros.
C
The graph crosses at both zeros.
D
The graph touches at $x=3$ and crosses at $x=-1$ .

Written response

1 point

Solve $\frac{5}{x-2}=\frac{2}{x+1}$ . Enter the solution value for $x$ .

Written response

1 point

For $f(x)=\frac{3x^2-4}{5x^2+x+1}$ , what is the value of the horizontal asymptote $y=\text{constant}$ ? Enter the constant as a decimal.

Written response

1 point

For the quadratic function $f(x)=-2x^2+8x-3$ , what is the x-coordinate of the vertex?

Open ended

1 point

Solve the polynomial inequality $(x-1)(x+2)^2>0$ . Use a sign chart or equivalent reasoning, and explain why each critical number is included or excluded.