Horizontal Translations (Shifts) from a Graph

Topics

Try VividMath Premium to unlock full access

Start Free Trial

Time limit: 0

Quiz summary

0 of 5 questions completed

Questions:

Information

–

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading...

You must sign in or sign up to start the quiz.

You have to finish following quiz, to start this quiz:

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 5

1. Question

Find the equation of the graph on the right of `f(x)=x^3 – 2x^2 +x`

Correct

Great Work!

Incorrect

Horizontal translations (shifts) of functions are written in the form `y=f(x+ color(royalblue)(h))`.

`color(royalblue)(h)` is how many units right or left the graph will be shifted.

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

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

To find the equation of the graph on the right of `f(x)=x^3 – 2x^2 +x`, count the number of units the graph is shifted over.

Count the number of units the graph is shifted over to the right.

The graph is shifted by `2` units.

Using the form `y=f(x+ color(royalblue)(h))` for horizontal translations and remembering that a shift to the right means `color(royalblue)(h)` is negative, the formula for the new graph to the right is `f(x)=(x color(royalblue)(-2))^3 – 2(x color(royalblue)(-2))^2 +(x color(royalblue)(-2))`

Then, we simplify the function by using the distributive property.

`f(x)`	`=`	`(x-2)^3 – 2(x-2)^2 +(x-2)`
	`=`	`(x-2)(x-2)(x-2)- 2(x-2)(x-2) +(x-2)`
	`=`	`(x-2)(x^2 -4x +4)- 2(x^2 -4x +4) +(x-2)`
	`=`	`x^3 – 4x^2 +4x – 2x^2 +8x – 8 -2x^2 + 8x – 8 + x – 2`
	`=`	`x^3 – 8x^2 + 21x -18`	Combining similar terms

Therefore, our simplified formula for the new graph to the right is `f(x)=x^3 – 8x^2 + 21x -18`

Question 2 of 5

2. Question
Find the equation of the graph on the left of `f(x)=x^2`
Correct

Great Work!

Incorrect

Horizontal translations (shifts) of functions are written in the form `y=f(x+ color(royalblue)(h))`.

`color(royalblue)(h)` is how many units right or left the graph will be shifted.

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

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

To find the equation of the graph on the left of `f(x)=x^2`, count the number of units the graph is shifted over.

Count the number of units the graph is shifted over to the left.

The graph is shifted by `3` units.

Using the form `y=f(x+ color(royalblue)(h))` for horizontal translations and remembering that a shift to the left means `color(royalblue)(h)` is positive, the formula for the new graph to the left is `f(x)=(x+ color(royalblue)(3))^2`
Question 3 of 5

3. Question
Find the equation of the graph on the left of `f(x)=\sqrt{x}`
Correct

Great Work!

Incorrect

Horizontal translations (shifts) of functions are written in the form `y=f(x+ color(royalblue)(h))`.

`color(royalblue)(h)` is how many units right or left the graph will be shifted.

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

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

To find the equation of the graph on the left of `f(x)=\sqrt{x}`, count the number of units the graph is shifted over.

Count the number of units the graph is shifted over to the left.

The graph is shifted by `4` units.

Using the form `y=f(x+ color(royalblue)(h))` for horizontal translations and remembering that a shift to the left means `color(royalblue)(h)` is positive, the formula for the new graph to the left is `f(x)=\sqrt{x+4}`
Question 4 of 5

4. Question
Find the equation of the graph on the right of `f(x)=2^x`
Correct

Great Work!

Incorrect

Horizontal translations (shifts) of functions are written in the form `y=f(x+ color(royalblue)(h))`.

`color(royalblue)(h)` is how many units right or left the graph will be shifted.

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

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

To find the equation of the graph on the left of `f(x)=2^x`, count the number of units the graph is shifted over.

Count the number of units the graph is shifted over to the right.

The graph is shifted by `3` units.

Using the form `y=f(x+ color(royalblue)(h))` for horizontal translations and remembering that a shift to the right means `color(royalblue)(h)` is negative, the formula for the new graph to the right is `f(x)=2^(x color(royalblue)(-3))`
Question 5 of 5

5. Question
Find the equation of the graph on the right of `f(x)=|x+2|`
Correct

Great Work!

Incorrect

Horizontal translations (shifts) of functions are written in the form `y=f(x+ color(royalblue)(h))`.

`color(royalblue)(h)` is how many units right or left the graph will be shifted.

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

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

To find the equation of the graph on the left of `f(x)=|x+2|`, count the number of units the graph is shifted over.

Count the number of units the graph is shifted over to the right.

The graph is shifted by `5` units.

Using the form `y=f(x+ color(royalblue)(h))` for horizontal translations and remembering that a shift to the right means `color(royalblue)(h)` is negative, the formula for the new graph to the left is `f(x)=|x+ 2 color(royalblue)(-5)|` or simply `f(x)=|x – 3|`