Horizontal Translations (Shifts) from a Point

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Question 1 of 3

1. Question
The point `(3,4)` lies on `y=f(x)`. Find the image point when it is horizontally translated (shifted) `2` units to the left.
- `(1,4)`
- `(5,4)`
- `(3,2)`
- `(3,6)`
Correct

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Incorrect

Horizontal translations (shifts) for coordinates (not functions).

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

Since we are translating the coordinates and not the function, when shifting left we subtract and when shifting right we add.

To translate (shift) the point `(3,4)` to the left by `2` units, subtract `color(red)(2)` from the `x` coordinate.

`(3,4)` Subtract `color(red)(2)` from the `x` coordinate. Remember `(x,y)`.

`=` `(3 color(red)(-2),4)` Simplify

`=` `(1,4)`

`(1,4)`
Question 2 of 3

2. Question
The point `P(6,4)` lies on `y=f(x)`. Find the image point when it is horizontally translated (shifted) `3` units to the right.
- `(9,4)`
- `(3,4)`
- `(6,1)`
- `(6,7)`
Correct

Great Work!

Incorrect

Horizontal translations (shifts) for coordinates (not functions).

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

Since we are translating the coordinates and not the function, when shifting left we subtract and when shifting right we add.

To translate (shift) the point `(6,4)` to the right by `3` units, add `color(forestgreen)(3)` to the `x` coordinate.

`(6,4)` Add `color(forestgreen)(3)` to the `x` coordinate. Remember `(x,y)`.

`=` `(6 color(forestgreen)(+3),4)` Simplify

`=` `(9,4)`

`(9,4)`
Question 3 of 3

3. Question
The point `(-3,4)` has already been translated (shifted) horizontally to the right by `5` units. Find the original point.
- `(2,4)`
- `(-8,4)`
- `(4,2)`
- `(4,-8)`
Correct

Great Work!

Incorrect

Horizontal translations (shifts) for coordinates (not functions).

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

Since we are translating the coordinates and not the function, when shifting left we subtract and when shifting right we add.

If we are finding the original point (we do the opposite). Shifting to the left we must add and shifting to the right we must subtract.

The point `(-3,4)` has already been translated (shifted) `5` units to the right along the `x`-axis.

To find the original point we must subtract `color(red)(5)` units and move towards the left from the `x` coordinate.

`(-3,4)` Subtract `color(red)(5)` from the `x` coordinate. Remember `(x,y)`.

`=` `(-3 color(red)(-5),4)` Simplify

`=` `(-8,4)`

`(-8,4)`

Horizontal Translations (Shifts) from a Point

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1. Question

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2. Question

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3. Question

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Quizzes

	`(3,4)`	Subtract `color(red)(2)` from the `x` coordinate. Remember `(x,y)`.
`=`	`(3 color(red)(-2),4)`	Simplify
`=`	`(1,4)`

	`(6,4)`	Add `color(forestgreen)(3)` to the `x` coordinate. Remember `(x,y)`.
`=`	`(6 color(forestgreen)(+3),4)`	Simplify
`=`	`(9,4)`

	`(-3,4)`	Subtract `color(red)(5)` from the `x` coordinate. Remember `(x,y)`.
`=`	`(-3 color(red)(-5),4)`	Simplify
`=`	`(-8,4)`