Graphing Rational Functions

Question 1

Which description matches the graph of f(x) = (8x)/(x + 5)?

Accepted Answer

vertical asymptote x = -5 and horizontal asymptote y = 8

Answer

vertical asymptote x = -5 and horizontal asymptote y = 0

Answer

vertical asymptote x = 8 and horizontal asymptote y = -5

Answer

vertical asymptote x = 5 and horizontal asymptote y = 8

Question 2

Which equation matches the graph?

Accepted Answer

y = 1/(x + 1)

Answer

y = 1/(x - 1)

Answer

y = 1/x + 1

Answer

y = (x + 1)/x

Question 3

At what point does the graph of f(x) = (x - 5)/(x - 4) cross the x-axis?

Accepted Answer

(5, 0)

Answer

(-5, 0)

Answer

(4, 0)

Answer

(0, 5/4)

Question 4

At what point does the graph of f(x) = (x - 6)/(x + 1) cross the x-axis?

Accepted Answer

(6, 0)

Answer

(-6, 0)

Answer

(-1, 0)

Answer

(0, -6)

Question 5

Which equation matches the graph?

Accepted Answer

y = 1/(x + 2)

Answer

y = 1/(x - 2)

Answer

y = 1/x + 2

Answer

y = (x + 2)/x

Question 6

Which equation matches the graph?

Accepted Answer

y = 1/(x - 4)

Answer

y = 1/(x + 4)

Answer

y = 1/x - 4

Answer

y = (x - 4)/x

Question 7

At what point does the graph of f(x) = (x + 1)/(x - 5) cross the x-axis?

Accepted Answer

(-1, 0)

Answer

(1, 0)

Answer

(5, 0)

Answer

(0, -1/5)

Question 8

Which equation produces the graph?

Accepted Answer

y = (x^2 - 16)/(x + 4)

Answer

y = (x^2 - 16)/(x - 4)

Answer

y = (x^2 + 16)/(x + 4)

Answer

y = (x + 4)/(x^2 - 16)

Question 9

Which equation matches the graph?

Accepted Answer

y = 1/(x + 3)

Answer

y = 1/(x - 3)

Answer

y = 1/x + 3

Answer

y = (x + 3)/x

Question 10

Which equation matches the graph?

Accepted Answer

y = 1/(x - 2)

Answer

y = 1/(x + 2)

Answer

y = 1/x - 2

Answer

y = (x - 2)/x

Question 11

Which description matches the graph of f(x) = (3x)/(x + 5)?

Accepted Answer

vertical asymptote x = -5 and horizontal asymptote y = 3

Answer

vertical asymptote x = -5 and horizontal asymptote y = 0

Answer

vertical asymptote x = 3 and horizontal asymptote y = -5

Answer

vertical asymptote x = 5 and horizontal asymptote y = 3

Question 12

Which equation matches the graph?

Accepted Answer

y = 1/(x - 3)

Answer

y = 1/(x + 3)

Answer

y = 1/x - 3

Answer

y = (x - 3)/x

Question 13

The graph of y = 1/x is shifted 4 units left and 2 units down. What is the equation of the image?

Accepted Answer

y = 1/(x + 4) - 2

Answer

y = 1/(x - 4) - 2

Answer

y = 1/(x + 4) + 2

Answer

y = 1/(x + 2) - 4

Question 14

The graph of y = 1/x is shifted 3 units left and 4 units down. What is the equation of the image?

Accepted Answer

y = 1/(x + 3) - 4

Answer

y = 1/(x - 3) - 4

Answer

y = 1/(x + 3) + 4

Answer

y = 1/(x + 4) - 3

Question 15

Which equation matches the graph?

Accepted Answer

y = 1/(x + 4)

Answer

y = 1/(x - 4)

Answer

y = 1/x + 4

Answer

y = (x + 4)/x

Question 16

A graph has a vertical asymptote at x = -1, a horizontal asymptote at y = 0, and passes through the point (1, 1/2). Which equation could it be?

Accepted Answer

y = 1/(x + 1)

Answer

y = 1/(x - 1)

Answer

y = 1/x + 1

Answer

y = (x + 1)/x

Question 17

The graph of y = 1/x is shifted 3 units left and 6 units down. What is the equation of the image?

Accepted Answer

y = 1/(x + 3) - 6

Answer

y = 1/(x - 3) - 6

Answer

y = 1/(x + 3) + 6

Answer

y = 1/(x + 6) - 3

Question 18

Which description matches the graph of f(x) = (5x)/(x + 2)?

Accepted Answer

vertical asymptote x = -2 and horizontal asymptote y = 5

Answer

vertical asymptote x = -2 and horizontal asymptote y = 0

Answer

vertical asymptote x = 5 and horizontal asymptote y = -2

Answer

vertical asymptote x = 2 and horizontal asymptote y = 5

Question 19

Which equation produces the graph?

Accepted Answer

y = (x^2 - 36)/(x + 6)

Answer

y = (x^2 - 36)/(x - 6)

Answer

y = (x^2 + 36)/(x + 6)

Answer

y = (x + 6)/(x^2 - 36)

Question 20

The graph of y = 1/x is shifted 4 units right and 2 units up. What is the equation of the image?

Accepted Answer

y = 1/(x - 4) + 2

Answer

y = 1/(x + 4) + 2

Answer

y = 1/(x - 4) - 2

Answer

y = 1/(x - 2) + 4

Question 21

At what point does the graph of f(x) = (x - 1)/(x + 6) cross the x-axis?

Accepted Answer

(1, 0)

Answer

(-1, 0)

Answer

(-6, 0)

Answer

(0, -1/6)

Question 22

Which description matches the graph of f(x) = (5x)/(x - 4)?

Accepted Answer

vertical asymptote x = 4 and horizontal asymptote y = 5

Answer

vertical asymptote x = 4 and horizontal asymptote y = 0

Answer

vertical asymptote x = 5 and horizontal asymptote y = 4

Answer

vertical asymptote x = -4 and horizontal asymptote y = 5

Question 23

Which description matches the graph of f(x) = (6x)/(x - 5)?

Accepted Answer

vertical asymptote x = 5 and horizontal asymptote y = 6

Answer

vertical asymptote x = 5 and horizontal asymptote y = 0

Answer

vertical asymptote x = 6 and horizontal asymptote y = 5

Answer

vertical asymptote x = -5 and horizontal asymptote y = 6

Question 24

Which equation produces the graph?

Accepted Answer

y = (x^2 - 4)/(x - 2)

Answer

y = (x^2 - 4)/(x + 2)

Answer

y = (x^2 + 4)/(x - 2)

Answer

y = (x - 2)/(x^2 - 4)

Question 25

The graph of y = 1/x is shifted 5 units right and 6 units down. What is the equation of the image?

Accepted Answer

y = 1/(x - 5) - 6

Answer

y = 1/(x + 5) - 6

Answer

y = 1/(x - 5) + 6

Answer

y = 1/(x + 6) + 5

Question 26

Which description matches the graph of f(x) = (4x)/(x - 1)?

Accepted Answer

vertical asymptote x = 1 and horizontal asymptote y = 4

Answer

vertical asymptote x = 1 and horizontal asymptote y = 0

Answer

vertical asymptote x = 4 and horizontal asymptote y = 1

Answer

vertical asymptote x = -1 and horizontal asymptote y = 4

Question 27

At what point does the graph of f(x) = (x + 5)/(x - 3) cross the x-axis?

Accepted Answer

(-5, 0)

Answer

(5, 0)

Answer

(3, 0)

Answer

(0, -5/3)

Question 28

A graph has a vertical asymptote at x = 3, a horizontal asymptote at y = 0, and passes through the point (4, 1). Which equation could it be?

Accepted Answer

y = 1/(x - 3)

Answer

y = 1/(x + 3)

Answer

y = 1/x - 3

Answer

y = (x - 3)/x

Question 29

Which description matches the graph of f(x) = (2x)/(x + 1)?

Accepted Answer

vertical asymptote x = -1 and horizontal asymptote y = 2

Answer

vertical asymptote x = -1 and horizontal asymptote y = 0

Answer

vertical asymptote x = 2 and horizontal asymptote y = -1

Answer

vertical asymptote x = 1 and horizontal asymptote y = 2

Question 30

Which description matches the graph of f(x) = (8x)/(x + 1)?

Accepted Answer

vertical asymptote x = -1 and horizontal asymptote y = 8

Answer

vertical asymptote x = -1 and horizontal asymptote y = 0

Answer

vertical asymptote x = 8 and horizontal asymptote y = -1

Answer

vertical asymptote x = 1 and horizontal asymptote y = 8

Question 31

Which description matches the graph of f(x) = (4x)/(x + 6)?

Accepted Answer

vertical asymptote x = -6 and horizontal asymptote y = 4

Answer

vertical asymptote x = -6 and horizontal asymptote y = 0

Answer

vertical asymptote x = 4 and horizontal asymptote y = -6

Answer

vertical asymptote x = 6 and horizontal asymptote y = 4

Question 32

Which equation matches the graph?

Accepted Answer

y = 1/(x - 1)

Answer

y = 1/(x + 1)

Answer

y = 1/x - 1

Answer

y = (x - 1)/x

Question 33

A graph has a vertical asymptote at x = -4, a horizontal asymptote at y = 0, and passes through the point (-3, 1). Which equation could it be?

Accepted Answer

y = 1/(x + 4)

Answer

y = 1/(x - 4)

Answer

y = 1/x + 4

Answer

y = (x + 4)/x

Question 34

At what point does the graph of f(x) = (x - 5)/(x + 6) cross the x-axis?

Accepted Answer

(5, 0)

Answer

(-5, 0)

Answer

(-6, 0)

Answer

(0, -5/6)

Question 35

Which equation matches the graph?

Accepted Answer

y = 1/(x - 6)

Answer

y = 1/(x + 6)

Answer

y = 1/x - 6

Answer

y = (x - 6)/x

Question 36

Which description matches the graph of f(x) = (7x)/(x + 5)?

Accepted Answer

vertical asymptote x = -5 and horizontal asymptote y = 7

Answer

vertical asymptote x = -5 and horizontal asymptote y = 0

Answer

vertical asymptote x = 7 and horizontal asymptote y = -5

Answer

vertical asymptote x = 5 and horizontal asymptote y = 7

Question 37

At what point does the graph of f(x) = (x + 3)/(x + 2) cross the x-axis?

Accepted Answer

(-3, 0)

Answer

(3, 0)

Answer

(-2, 0)

Answer

(0, 3/2)

Question 38

The graph of y = 1/x is shifted 3 units right and 4 units down. What is the equation of the image?

Accepted Answer

y = 1/(x - 3) - 4

Answer

y = 1/(x + 3) - 4

Answer

y = 1/(x - 3) + 4

Answer

y = 1/(x + 4) + 3

Question 39

Which description matches the graph of f(x) = (2x)/(x + 3)?

Accepted Answer

vertical asymptote x = -3 and horizontal asymptote y = 2

Answer

vertical asymptote x = -3 and horizontal asymptote y = 0

Answer

vertical asymptote x = 2 and horizontal asymptote y = -3

Answer

vertical asymptote x = 3 and horizontal asymptote y = 2

Question 40

Which description matches the graph of f(x) = (4x)/(x - 2)?

Accepted Answer

vertical asymptote x = 2 and horizontal asymptote y = 4

Answer

vertical asymptote x = 2 and horizontal asymptote y = 0

Answer

vertical asymptote x = 4 and horizontal asymptote y = 2

Answer

vertical asymptote x = -2 and horizontal asymptote y = 4

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Graphing Rational Functions

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Graphing Rational Functions

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner