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Horizontal Translations (Shifts)>
Horizontal Translations (Shifts) 1Horizontal Translations (Shifts) 1
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Question 1 of 7
1. Question
Given the parent function `y=x^2`
Which of the following is the graph of `y=(x+3)^2`?
Correct
Great Work!
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Horizontal translations (shifts) of functions are written in the form `y=(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 LeftFor the equation: `y=(x color(royalblue)(+3))^2`, the value of `color(royalblue)(h)` is positive which means we translate (shift) the graph to the left by `color(royalblue)(3)` units.Use a table of values to find at least four points on the function `y=x^2`.`x` `-4` `-3` `-2` `-1` `0` `1` `2` `3` `y` `16` `9` `4` `1` `0` `1` `4` `9` Sketch the graph of `y=x^2` using the table of values.Since `h` is positive for `y=(x color(royalblue)(+3))^2` we will translate the graph to the left by `color(royalblue)(3)` units.
Sketch the graph of `y=(x+3)^2` by following the shape of the original graph but connecting the new translated points.
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Question 2 of 7
2. Question
Given the parent function `y=2^x`
Which of the following is the graph of `y=2^(x+2)`?
Correct
Great Work!
Incorrect
Horizontal translations (shifts) of functions are written in the form `y=(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 LeftFor the equation: `y=2^(x color(royalblue)(+2))`, the value of `color(royalblue)(h)` is positive which means we translate (shift) the graph to the left by `color(royalblue)(2)` units.Use a table of values to find at least four points on the function `y=2^x`.`x` `-4` `-2` `-1` `0` `1` `2` `3` `y` `1/2^4` `1/4` `1/2` `1` `2` `4` `8` Sketch the graph of `y=2^x` using the table of values.Since `h` is positive for `y=2^(x color(royalblue)(+2))` we will translate the graph to the left by `color(royalblue)(2)` units.
Sketch the graph of `y=2^(x+2)` by following the shape of the original graph but connecting the new translated points.
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Question 3 of 7
3. Question
Given the parent function `y=\sqrt(x)`
Which of the following is the graph of `y=\sqrt(x-3)`?
Correct
Great Work!
Incorrect
Horizontal translations (shifts) of functions are written in the form `y=(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 LeftFor the equation: `y=\sqrt(x color(royalblue)(-3))`, the value of `color(royalblue)(h)` is negative which means we translate (shift) the graph to the right by `color(royalblue)(3)` units.Use a table of values to find at least four points on the function `y=\sqrt(x)`.`x` `-1` `0` `1` `2` `3` `4` `6` `y` `X` `0` `1` `1.4` `1.7` `2` `2.5` Sketch the graph of `y=x^2` using the table of values.Since `h` is negative for `y=\sqrt(x color(royalblue)(-3))` we will translate the graph to the right by `color(royalblue)(3)` units.
Sketch the graph of `y=\sqrt(x-3)` by following the shape of the original graph but connecting the new translated points.
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Question 4 of 7
4. Question
Given the parent function `y=|x|`
Which of the following is the graph of `y=|x+4|`?
Correct
Great Work!
Incorrect
Horizontal translations (shifts) of functions are written in the form `y=(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 LeftFor the equation: `y=|x color(royalblue)(+4)|`, the value of `color(royalblue)(h)` is positive which means we translate (shift) the graph to the left by `color(royalblue)(4)` units.Use a table of values to find at least four points on the function `y=|x|`.`x` `-4` `-3` `-2` `-1` `0` `1` `2` `3` `y` `4` `3` `2` `1` `0` `1` `2` `3` Sketch the graph of `y=|x|` using the table of values.Since `h` is positive for `y=|x color(royalblue)(+4)|` we will translate the graph to the left by `color(royalblue)(4)` units.
Sketch the graph of `y=|x+4|` by following the shape of the original graph but connecting the new translated points.
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Question 5 of 7
5. Question
Given the parent function `y=x^3`
Which of the following is the graph of `y=(x-4)^3`?
Correct
Great Work!
Incorrect
Horizontal translations (shifts) of functions are written in the form `y=(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 LeftFor the equation: `y=(x color(royalblue)(-4))^3`, the value of `color(royalblue)(h)` is negative which means we translate (shift) the graph to the right by `color(royalblue)(4)` units.Use a table of values to find at least four points on the function `y=x^3`.`x` `-2` `-1` `0` `1` `2` `y` `-8` `-1` `0` `1` `8` Sketch the graph of `y=x^3` using the table of values.Since `h` is negative for `y=(x color(royalblue)(-4))^3` we will translate the graph to the right by `color(royalblue)(4)` units.
Sketch the graph of `y=(x-4)^3` by following the shape of the original graph but connecting the new translated points.
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Question 6 of 7
6. Question
Given the parent function `y=log x`
Which of the following is the graph of `y=log(x+5)`?
Correct
Great Work!
Incorrect
Horizontal translations (shifts) of functions are written in the form `y=(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 LeftFor the equation: `y=log(x color(royalblue)(+5))`, the value of `color(royalblue)(h)` is positive which means we translate (shift) the graph to the left by `color(royalblue)(5)` units.Use a table of values to find at least four points on the function `y=logx`.`x` `1/2` `1` `2` `3` `6` `8` `y` `-0.3` `0` `0.3` `0.5` `0.8` `0.9` Sketch the graph of `y=logx` using the table of values.Since `h` is positive for `y=log(x color(royalblue)(+5))` we will translate the graph to the left by `color(royalblue)(5)` units.
Sketch the graph of `y=log(x+5)` by following the shape of the original graph but connecting the new translated points.
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Question 7 of 7
7. Question
Given the parent function `y=1/x`
Which of the following is the graph of `y=1/(x-3)`?
Correct
Great Work!
Incorrect
Horizontal translations (shifts) of functions are written in the form `y=(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 LeftFor the equation: `y=1/(x color(royalblue)(-3))`, the value of `color(royalblue)(h)` is negative which means we translate (shift) the graph to the right by `color(royalblue)(3)` units.Use a table of values to find at least four points on the function `y=1/x`.`x` `-4` `-3` `-2` `-1` `1` `2` `3` `y` `-1/4` `-1/3` `-1/2` `-1` `1` `1/2` `1/3` Sketch the graph of `y=1/x` using the table of values.
Since `h` is negative for `y=1/(x color(royalblue)(-3))` we will translate the graph to the right by `color(royalblue)(3)` units.
Sketch the graph of `y=1/(x-3)` by following the shape of the original graph but connecting the new translated points.
Quizzes
- Vertical Translations (Shifts) 1
- Vertical Translations (Shifts) 2
- Vertical Translations (Shifts) from a Point
- Horizontal Translations (Shifts) 1
- Horizontal Translations (Shifts) from a Point
- Horizontal Translations (Shifts) from a Graph
- Horizontal and Verticals Translations (Shifts) from a Graph
- Sketch a Graph using Translations (Shifts)
- Write the Equation from a Graph
- Write the Equation from Translations (Shifts) 1
- Vertical Dilations (Stretch/Shrink)
- Horizontal Dilations (Stretch/Shrink) 1
- Horizontal Dilations (Stretch/Shrink) 2
- Horizontal Dilations (Stretch/Shrink) – Scale Factor
- Horizontal and Vertical Dilations (Stretch/Shrink) 1
- Horizontal and Vertical Dilations (Stretch/Shrink) 2
- Horizontal and Vertical Dilations (Stretch/Shrink) 3
- Graphing Reflections 1
- Graphing Reflections 2
- Reflection with Rotation
- Combinations of Transformations: Order
- Combinations of Transformations: Coordinates
- Combinations of Transformations: Find Equation 1
- Combinations of Transformations: Find Equation 2
- Combinations of Transformations: Find Equation 3