Free Printable Rational Function

1.

What is the domain of the rational function $f\left(x\right)=\frac{1}{x-2}$ ?

a)

All real numbers except 2

b)

All real numbers except 0

c)

All real numbers

d)

All positive real numbers

2.

Which of the following is a vertical asymptote of the rational function $g\left(x\right)=\ \frac{x^2-4}{x+2}$ ?

a)

x = -2

b)

x = 2

c)

y = -2

d)

y = 2

3.

What is the horizontal asymptote of the rational function $h\left(x\right)=\frac{2x^3-5x^2+3}{x^3+x^2-2x}$ ?

a)

y = 0

b)

y = 1

c)

y = 2

d)

y = 2x

4.

If the graph of a rational function crosses the x-axis at $x=3$ and $x=-1$ , what can be said about the function?

a)

The function has no vertical asymptotes.

b)

The function has a hole at $x=2$ .

c)

The function has a horizontal asymptote at $y=0$ .

d)

The function has a vertical asymptote at $x=3$ and $x=-1$ .

5.

What is the degree of the numerator in the rational function $R\left(x\right)=\frac{3x^4+2x^3-5x^2+7}{2x^2-1}$ ?

a)

4

b)

3

c)

2

d)

1

6.

Which of the following is a possible hole in the graph of the rational function $S\left(x\right)=\frac{x^2-4}{x+2}$ ?

a)

x=-2

b)

x=2

c)

x=-4

d)

x=0

7.

What is the slant (or oblique) asymptote of the rational function $T\left(x\right)=\frac{3x^2+2x-5}{x+1}$ ?

a)

y = 3x - 1

b)

y = 2x + 3

c)

y = 3x

d)

There is no slant asymptote.

8.

When simplifying a rational function, what is the first step to find the vertical asymptotes?

a)

Factor the numerator and denominator.

b)

Find the common factors of the numerator and denominator.

c)

Set the denominator equal to zero and solve for x.

d)

Divide the numerator by the denominator.

9.

What is a rational function?

a)

A function with a square root.

b)

A function with a rational exponent.

c)

A function that can be expressed as a ratio of two polynomials.

d)

A function with complex roots.

10.

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

a)

y=3

b)

y=2

c)

y=1

d)

y=0

Rational Function

Total questions: 10

Worksheet time: 6mins

Similar Resources on Wayground