Free Practice Quiz Question List

03/10 Rational Functions Online Quiz Questions

Use this free practice quiz with 20 questions to review 03/10 Rational Functions, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Which statement correctly defines a rational function?

A
A function whose numerator and denominator must both be linear
B
A quotient of polynomials with a denominator that is not zero
C
Any function containing a square root
D
A polynomial with no restrictions

Choose one

1 point

For $\frac{x^2-9}{x^2-3x}$ , which domain restrictions must be stated after simplifying?

A
x cannot equal 0 or 3
B
x cannot equal 0 only
C
x cannot equal 3 only
D
There are no domain restrictions

Choose one

1 point

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

A
y = 3
B
y = 1
C
y = 0
D
There is no horizontal asymptote

Choose one

1 point

For $f(x)=\frac{x^2-1}{(x-1)(x+2)}$ , which description of the discontinuities is correct?

A
A vertical asymptote at x = 1 and a hole at x = -2
B
A hole at x = 1 and a vertical asymptote at x = -2
C
Vertical asymptotes at both x = 1 and x = -2
D
Holes at both x = 1 and x = -2

Choose all

1 point

Select all statements that correctly describe discontinuities of rational functions.

A
A canceled denominator factor can create a hole.
B
A denominator zero is always a vertical asymptote.
C
A remaining denominator factor can create a vertical asymptote.
D
A hole restores the excluded input to the domain.

Choose all

1 point

Which steps or rules are valid when solving a rational inequality with a sign chart? Select all that apply.

A
Find zeros of the numerator.
B
Find zeros of the denominator.
C
Include every denominator zero in the solution when the inequality is non-strict.
D
Test signs on the intervals determined by the critical numbers.

True or false

1 point

True or false: If a factor in the denominator cancels with a factor in the numerator, the corresponding excluded input creates a hole rather than a vertical asymptote.

A
True
B
False

True or false

1 point

True or false: A graph of a rational function can never cross a horizontal asymptote.

A
True
B
False

Written response

1 point

For $f(x)=\frac{2x+1}{(x-4)(x+2)}$ , what is the positive restricted x-value?

Written response

1 point

For $g(x)=\frac{4x^2+1}{2x^2-7}$ , enter the value of the horizontal asymptote $y=$ .

Fill in the blank

1 point

To simplify a rational expression, first the numerator and denominator completely.

Fill in the blank

1 point

In a rational inequality, zeros of the numerator and are called ; denominator zeros are excluded from the final solution.

Choose one

1 point

What is the x-intercept of $f(x)=\frac{x-2}{x+1}$ ?

A
(2, 0)
B
(-1, 0)
C
(0, -2)
D
(1, 0)

True or false

1 point

True or false: The y-intercept of $f(x)=\frac{x-2}{x+1}$ is $(0,-2)$ .

A
True
B
False

Choose one

1 point

What asymptote is obtained by polynomial division for $h(x)=\frac{x^2+1}{x-1}$ ?

A
y = 0
B
y = 1
C
y = x + 1
D
x = 1

Choose one

1 point

After simplifying $\frac{x^2-9}{x^2-3x}$ , which restrictions must still be stated for the original expression?

A
x≠0
B
x≠0,3
C
x≠3
D
All real numbers

Written response

1 point

For $g(x)=\frac{4x^2+1}{2x^2-7}$ , enter the value of the horizontal asymptote $y=\text{value}$ .

Choose one

1 point

For $f(x)=\frac{x-2}{x+1}$ , which set of features is correct?

A
Vertical asymptote x=1, x-intercept (-2,0), y-intercept (0,2)
B
Vertical asymptote x=-1, x-intercept (-2,0), y-intercept (0,-2)
C
Vertical asymptote x=-1, x-intercept (2,0), y-intercept (0,-2)
D
Vertical asymptote x=2, x-intercept (-1,0), y-intercept (0,1)

Written response

1 point

What type of discontinuity is created by a common factor that cancels from the numerator and denominator of a rational function?

Open ended

1 point

Solve $\frac{3}{x-2}-\frac{1}{x+1}=2$ . Show how you determine the restrictions, clear the denominators, and check whether each resulting solution is valid.