Free Practice Quiz Question List

09/14 9. Rational Expressions and Functions Online Quiz Questions

Use this free practice quiz with 20 questions to review 09/14 9. Rational Expressions and Functions, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

What are the restrictions on $x$ for the rational expression $\frac{x+4}{x^2-9}$ ?

A
$x\ne -9,9$
B
$x\ne -3$ only
C
$x\ne -3,3$
D
There are no restrictions

True or false

1 point

True or false: If a factor causing a zero denominator is canceled while simplifying a rational expression, that restricted value becomes part of the original function's domain.

A
True
B
False

Written response

1 point

Solve the proportion $\frac{x}{12}=\frac{5}{8}$ . Enter the value of $x$ as a decimal.

Fill in the blank

1 point

Complete the numerator in the sum $\frac{2}{x-1}+\frac{3}{x+2}=\frac{$ $}{(x-1)(x+2)}$ .

Choose one

1 point

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

A
$y=x+1$
B
$y=x+3$
C
$y=3x+1$
D
$y=0$

Choose all

1 point

Select all statements that are true for $R(x)=\frac{(x-2)(x+1)}{(x-2)(x-3)}$ .

A
The graph has a hole at $(2,-3)$ .
B
The vertical asymptote is $x=3$ .
C
The domain excludes $x=2$ and $x=3$ .
D
The horizontal asymptote is $y=1$ .
E
The graph has an $x$ -intercept at $(2,0)$ .

Fill in the blank

1 point

One pump empties a tank in $6$ hours and another empties it in $10$ hours. Complete the statement with the reduced fractional time: Together, they empty the tank in hours.

Written response

1 point

A company's average cost per item is $A(x)=\frac{18{,}000}{x}+12$ . What is $A(600)$ , in dollars per item?

True or false

1 point

True or false: For $R(x)=\frac{(x-2)(x+1)}{(x-2)(x-3)}$ , the graph includes a point at $x=2$ but cannot cross the vertical asymptote $x=3$ .

A
True
B
False

Choose all

1 point

Select all valid reasons for rejecting a solution to a rational equation or rational-model application.

A
It makes a denominator equal to zero.
B
It represents a negative time, rate, distance, or quantity when that quantity must be positive.
C
It fails when substituted into the original equation or model.
D
It is written as a decimal instead of a fraction.
E
It is not the largest numerical solution.

Open ended

1 point

A car travels $240$ miles. It travels the first $120$ miles at speed $r$ and the remaining $120$ miles at speed $r+20$ . The total travel time is $5$ hours. Set up and solve a rational equation, reject any nonphysical solution, and report both speeds with units.

Choose one

1 point

What are the intercepts of $R(x)=\frac{x+1}{x-2}$ ?

A
The $x$ -intercept is $(1,0)$ , and the $y$ -intercept is $(0,\frac{1}{2})$ .
B
The $x$ -intercept is $(-1,0)$ , and the $y$ -intercept is $(0,-\frac{1}{2})$ .
C
The $x$ -intercept is $(2,0)$ , and there is no $y$ -intercept.
D
There are no intercepts because the function is rational.

True or false

1 point

True or false: A rational-function graph may cross a horizontal or slant asymptote.

A
True
B
False

Choose one

1 point

What restrictions must be placed on the variable in the rational expression $\frac{x+4}{x^2-9}$ ?

A
$x\ne 9$
B
$x\ne 3$ and $x\ne -3$
C
$x\ne 0$ and $x\ne 9$
D
There are no restrictions

Written response

1 point

Solve the proportion $\frac{x}{12}=\frac{5}{8}$ . Enter the numerical value of $x$ .

Choose one

1 point

Simplify $\frac{2}{x-1}+\frac{3}{x+2}$ .

A
$\frac{5x+1}{(x-1)(x+2)}$
B
$\frac{5x+5}{(x-1)(x+2)}$
C
$\frac{5x+1}{x+1}$
D
$\frac{5}{2x+1}$

Written response

1 point

What term names the line $x=a$ that a rational-function graph approaches near a remaining denominator zero?

Choose one

1 point

Solve $\frac{3}{x}+\frac{2}{x-1}=1$ .

A
$x=0$ and $x=1$
B
$x=3$ and $x=-3$
C
$x=3+\sqrt6$ and $x=3-\sqrt6$
D
$x=6+\sqrt3$ and $x=6-\sqrt3$

Choose one

1 point

For $R(x)=\frac{2x^2+3x-2}{x^2-4}$ , which list correctly identifies the hole, vertical asymptote, and horizontal asymptote?

A
Hole at $x=2$ , vertical asymptote $x=-2$ , horizontal asymptote $y=0$
B
Hole at $x=-2$ , vertical asymptote $x=2$ , horizontal asymptote $y=2$
C
No hole, vertical asymptote $x=2$ , horizontal asymptote $y=0$
D
Hole at $x=-2$ , vertical asymptote $x=-2$ , horizontal asymptote $y=1$

Choose one

1 point

One pump empties a tank in 6 hours and another empties it in 10 hours. How long do they take to empty the tank together?

A
$\frac{15}{4}$ hours
B
$\frac{4}{15}$ hours
C
8 hours
D
16 hours