Write the Equation from a Graph

Years

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 2

1. Question
Find the equation of the function below by using the graph for $y=x^3$ .
- 1. $y=(x-3)^3 -1$
- 2. $y=(x+3)^3 +1$
- 3. $y=(x-3)^3 +1$
- 4. $y=(x+3)^3 -1$
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Horizontal and vertical translations of cubic functions are written in the form $y=(x-color(red)(h))^3 + color(blue)(c)$ where the point $(color(red)(h),color(blue)(c))$ is the vertex of the function.

$color(red)(-h)$ is a shift to the right and $color(blue)(+c)$ is a shift upwards.

$(-h) \ bb(rarr)$ Shift Right

$(+h) \ bb(larr)$ Shift Left

$(-c) \ bb(darr)$ Shift Down

$(+c) \ bb(uarr)$ Shift Up

To obtain the equation of the function by using the graph for $y=x^3$ , first sketch the function $y=x^3$ .

Sketch the function $y=x^3$ . Remember the formula $y=(x-color(red)(h))^3 + color(blue)(c)$ when applied to $y=x^3$ (can be rewritten as $y=(x-color(red)(0))^3+color(blue)(0)$ ) has its vertex at $(color(red)(0),color(blue)(0))$ .

To find the horizontal shift ( $h$ ), count the units between the graphs along the $x$ -axis. It is $3$ units to the right ( $h=3$ ).

To find the vertical shift ( $c$ ), count the units between the graphs along the $y$ -axis. It is $1$ unit down ( $c=-1$ ).

Put the equation together using the formula $y=(x-color(red)(h))^3 + color(blue)(c)$ , $color(red)(h=3)$ , and $color(blue)(c=-1)$ . The unknown graph is $y=(x-color(red)(3))^3 color(blue)(-1)$ .

$y=(x-3)^3 -1$
Question 2 of 2

2. Question
Find the equation of the function below by using the graph for $y=1/x$ .
- 1. $y=1/(x+3)-2$
- 2. $y=1/(x-3)+2$
- 3. $y=1/(x+2)-3$
- 4. $y=1/(x-2)+3$
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Horizontal and vertical translations of hyperbolic functions are written in the form $y=1/(x-color(red)(h)) +color(blue)(c)$ where the point $(color(red)(h),color(blue)(c))$ is the intersection point of the asymptotes of the function.

$color(red)(-h)$ is a shift to the right and $color(blue)(+c)$ is a shift upwards.

$(-h) \ bb(rarr)$ Shift Right

$(+h) \ bb(larr)$ Shift Left

$(-c) \ bb(darr)$ Shift Down

$(+c) \ bb(uarr)$ Shift Up

To obtain the equation of the function by using the graph for $y=1/x$ , first sketch the function $y=1/x$ .

Sketch the function $y=1/x$ . Remember the formula $y=1/(x-color(red)(h)) +color(blue)(c)$ when applied to $y=1/x$ (can be rewritten as $y=1/(x-color(red)(0))+color(blue)(0)$ ) has the intersection point of the asymptotes at $(color(red)(0),color(blue)(0))$ .

To find the horizontal shift ( $h$ ), count the units between the graphs along the $x$ -axis. It is $2$ units to the right ( $h=2$ ).

To find the vertical shift ( $c$ ), count the units between the graphs along the $y$ -axis. It is $3$ units up ( $c=3$ ).

Put the equation together using the formula $y=1/(x-color(red)(h)) +color(blue)(c)$ , $color(red)(h=2)$ , and $color(blue)(c=3)$ . The unknown graph is $y=1/(x-color(red)(2))+color(blue)(3)$ .

$y=1/(x-2)+3$

Write the Equation from a Graph

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Great Work!

2. Question

Great Work!

Quizzes