1. Which response represents the solution to the rational equation below? 1 x − 4 + 6 x = 3 x \frac{1}{x-4}+\frac{6}{x}=\frac{3}{x} x − 4 1 + x 6 = x 3

x = 0 , x = 4 x=0,\ x=4 x = 0 , x = 4

x = 0 , x = 3 x=0,\ x=3 x = 0 , x = 3

The equation for g(x) was obtained by transforming f ( x ) = 1 x f\left(x\right)=\frac{1}{x} f ( x ) = x 1 . Which description best describes the transformations performed on f(x) to obtain g(x)? g ( x ) = 2 x + 16 g\left(x\right)=\frac{2}{x+16} g ( x ) = x + 1 6 2

Vertical stretch by a factor of 1 2 \frac{1}{2} 2 1 followed by a horizontal translation right 16 units.

Vertical stretch by a factor of 1 2 \frac{1}{2} 2 1 followed by a vertical translation up 16 units.

The function g(x) was obtained by transforming f ( x ) = 1 x . f\left(x\right)=\frac{1}{x}. f ( x ) = x 1 . The function f ( x ) f\left(x\right) f ( x ) is reflected about the x-axis then translated up 12 units. Which equation represents g ( x ) ? g\left(x\right)? g ( x ) ?

g ( x ) = − 1 x + 12 g\left(x\right)=-\frac{1}{x}+12 g ( x ) = − x 1 + 1 2

g ( x ) = 1 x − 12 g\left(x\right)=\frac{1}{x-12} g ( x ) = x − 1 2 1

g ( x ) = − 1 x + 12 g\left(x\right)=-\frac{1}{x+12} g ( x ) = − x + 1 2 1

g ( x ) = 1 x − 12 g\left(x\right)=\frac{1}{x}-12 g ( x ) = x 1 − 1 2

A small private airplane traveled 140 miles in the same amount of time it took a helicopter to travel 95 miles. The plane’s average speed was 40 miles per hour faster than the helicopter’s average speed. Which equation could be used to calculate the average speed of each vehicle?

140 x + 40 = 95 x \frac{140}{x+40}=\frac{95}{x} x + 4 0 1 4 0 = x 9 5

95 x + 40 = 140 x \frac{95}{x+40}=\frac{140}{x} x + 4 0 9 5 = x 1 4 0

140 x = 95 x + 40 140x=95x+40 1 4 0 x = 9 5 x + 4 0

40 x = 235 40x=235 4 0 x = 2 3 5

Which response represents the solution to the rational equation below? 2 x − 3 = x x + 3 \frac{2}{x-3}=\frac{x}{x+3} x − 3 2 = x + 3 x

x = − 1 , x = 6 x=-1,x=6 x = − 1 , x = 6

x = − 2 , x = 3 x=-2,x=3 x = − 2 , x = 3

x = − 3 , x = 3 x=-3,x=3 x = − 3 , x = 3

Rational Functions - Review

Authored by Sharon Bryant

Mathematics

9th - 11th Grade

CCSS covered

Used 12+ times

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

Content View
Student View

20 questions

Show all answers

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

1. Which response represents the solution to the rational equation below?

$\frac{1}{x-4}+\frac{6}{x}=\frac{3}{x}$

$x=0,\ x=4$

$x=3$

$x=0,\ x=3$

$x=4$

Tags

CCSS.HSA.REI.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The amount of time needed to stuff and address envelopes for the local high school’s fundraising campaign varies inversely with the number of student and parent volunteers that attend the envelope stuffing event. Last year, it took 20 people 3 hours to stuff and address the envelopes.

Select the equation that could be used to estimate the amount of time, y, it will take x number of volunteers to stuff and address the same number of envelopes.

y=\frac{7}{x}

$y=60x$

$y=\frac{60}{x}$

$y=7x$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The amount of time needed to stuff and address envelopes for the local high school’s fundraising campaign varies inversely with the number of student and parent volunteers that attend the envelope stuffing event. Last year, it took 20 people 3 hours to stuff and address the envelopes.

How many volunteers are needed to stuff and address all the envelopes in 2 hours?

10 volunteers

30 volunteers

20 volunteers

40 volunteers

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Multiply the rational expression below and record any excluded values.

$\frac{x^2+7x+6}{x^2+x-2}\cdot\frac{x^2-x-6}{x^2+3x-18}$

$1,x≠-6,-2,1,3$

$\frac{x(x+1)}{(x-1)(x+2)}\ ,x≠-6,-2,1,3$

$\frac{(x+1)(x+7)}{(x-1)(x-6)},x≠1,2,3,6$

$\frac{X+1}{X-1},x≠-6,-2,1,3$

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the vertical asymptote of the function below?

$f\left(x\right)=\frac{x^2-2x-8}{x^2+2x-24}$

$y=1$

$x=4$

$x=-2$

$x=-6$

Tags

CCSS.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which response represents the solution to the rational equation below?

$\frac{5}{x+8}=\frac{2}{x-1}$

$x=7$

$x=3$

$x=-8$

$x=0$

Tags

CCSS.HSA.REI.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

A young entrepreneur purchased a custom-painted lemonade stand for $30. Each cup of lemonade sold costs $0.25 in materials. Let x=number of lemonade cups sold. Which function represents the average cost, c, of a cup of lemonade?

$c(x)=\frac{30+0.25x}{x}$

$c(x)=\frac{30}{x}$

$c(x)=30+0.25x$

$c(x)=0.25x$

Tags

CCSS.HSF-BF.A.1A

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The equation for g(x) was obtained by transforming $f\left(x\right)=\frac{1}{x}$ . Which description best describes the transformations performed on f(x) to obtain g(x)?

$g\left(x\right)=\frac{2}{x+16}$

Vertical stretch by a factor of $\frac{1}{2}$ followed by a horizontal translation right 16 units.

Vertical stretch by a factor of $\frac{1}{2}$ followed by a vertical translation up 16 units.

Vertical stretch by a factor of 2 followed by a horizontal translation left 16 units.

Vertical stretch by a factor of 2 followed by a vertical translation down 16 units.

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The function g(x) was obtained by transforming $f\left(x\right)=\frac{1}{x}.$ The function $f\left(x\right)$ is reflected about the x-axis then translated up 12 units. Which equation represents $g\left(x\right)?$

$g\left(x\right)=\frac{1}{x-12}$

$g\left(x\right)=-\frac{1}{x+12}$

$g\left(x\right)=-\frac{1}{x}+12$

$g\left(x\right)=\frac{1}{x}-12$

Tags

CCSS.HSF.BF.B.3

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The graph of a function passes through the point (3, 8). If y varies inversely as x, write a function relating x and y.

y=\frac{24}{x}

$y=11x$

$y=\frac{11}{x}$

$y=24x$

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Microsoft

or continue with

Facebook

Apple

Others

By signing up, you agree to our Terms of Service & Privacy Policy

Already have an account?

Similar Resources on Wayground

15 questions

Year 10 Solving Equations

Quiz

•

9th - 11th Grade

16 questions

Area of right angled and non right angled triangles

Quiz

•

10th Grade

16 questions

Prueba inicial 4º ESO Académicas

Quiz

•

10th Grade

20 questions

Me divierto con las Matemáticas LILEGRE 8° y 9° 2020.

Quiz

•

1st Grade - University

20 questions

DRAGÕES E FUNÇÕES

Quiz

•

10th Grade

20 questions

Thử thách Toán Tuần 11

Quiz

•

5th Grade - University

20 questions

Mnożenie do 50

Quiz

•

1st - 12th Grade

20 questions

Areas related to circle

Quiz

•

10th Grade

Popular Resources on Wayground

10 questions

How much do you know about our Portrait of an Eagle?

Quiz

•

10th Grade

10 questions

Fast Food Slogans

Quiz

•

6th - 8th Grade

21 questions

Continents and Oceans

Quiz

•

6th Grade

20 questions

Parts of Speech

Quiz

•

5th Grade

16 questions

Subject & Predicate

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

12 questions

Map Skills

Quiz

•

3rd Grade

22 questions

Continents and Oceans

Quiz

•

5th Grade

Discover more resources for Mathematics

20 questions

Graphing Inequalities on a Number Line

Quiz

•

6th - 9th Grade

10 questions

Translating Algebraic Expressions

Quiz

•

9th Grade

20 questions

Exponent Rules

Quiz

•

8th - 9th Grade

20 questions

Function or Not a Function

Quiz

•

8th - 9th Grade

10 questions

Literal Equations

Quiz

•

9th Grade

18 questions

Discrete Vs. Continuous Practice

Quiz

•

9th Grade

10 questions

Solving Absolute Value Equations

Quiz

•

9th Grade

10 questions

Identifying equations

Quiz

•

KG - University

Rational Functions - Review

1. Which response represents the solution to the rational equation below? 1x−4+6x=3x\frac{1}{x-4}+\frac{6}{x}=\frac{3}{x}x−41​+x6​=x3​

Multiply the rational expression below and record any excluded values. x2+7x+6x2+x−2⋅x2−x−6x2+3x−18\frac{x^2+7x+6}{x^2+x-2}\cdot\frac{x^2-x-6}{x^2+3x-18}x2+x−2x2+7x+6​⋅x2+3x−18x2−x−6​

What is the vertical asymptote of the function below? f(x)=x2−2x−8x2+2x−24f\left(x\right)=\frac{x^2-2x-8}{x^2+2x-24}f(x)=x2+2x−24x2−2x−8​

Which response represents the solution to the rational equation below? 5x+8=2x−1\frac{5}{x+8}=\frac{2}{x-1}x+85​=x−12​

A young entrepreneur purchased a custom-painted lemonade stand for $30. Each cup of lemonade sold costs $0.25 in materials. Let x=number of lemonade cups sold. Which function represents the average cost, c, of a cup of lemonade?

The equation for g(x) was obtained by transforming f(x)=1xf\left(x\right)=\frac{1}{x}f(x)=x1​ . Which description best describes the transformations performed on f(x) to obtain g(x)? g(x)=2x+16g\left(x\right)=\frac{2}{x+16}g(x)=x+162​

The function g(x) was obtained by transforming f(x)=1x.f\left(x\right)=\frac{1}{x}.f(x)=x1​. The function f(x)f\left(x\right)f(x) is reflected about the x-axis then translated up 12 units. Which equation represents g(x)?g\left(x\right)?g(x)?

The graph of a function passes through the point (3, 8). If y varies inversely as x, write a function relating x and y.

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

1. Which response represents the solution to the rational equation below?

$\frac{1}{x-4}+\frac{6}{x}=\frac{3}{x}$

Multiply the rational expression below and record any excluded values.

$\frac{x^2+7x+6}{x^2+x-2}\cdot\frac{x^2-x-6}{x^2+3x-18}$

What is the vertical asymptote of the function below?

$f\left(x\right)=\frac{x^2-2x-8}{x^2+2x-24}$

Which response represents the solution to the rational equation below?

$\frac{5}{x+8}=\frac{2}{x-1}$

The equation for g(x) was obtained by transforming $f\left(x\right)=\frac{1}{x}$ . Which description best describes the transformations performed on f(x) to obtain g(x)?

$g\left(x\right)=\frac{2}{x+16}$

The function g(x) was obtained by transforming $f\left(x\right)=\frac{1}{x}.$ The function $f\left(x\right)$ is reflected about the x-axis then translated up 12 units. Which equation represents $g\left(x\right)?$