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Vertical Translations (Shifts)>
Vertical Translations (Shifts) 1Vertical Translations (Shifts) 1
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Question 1 of 7
1. Question
The graph below is `y=f(x)`
Sketch `y=f(x)-3`
Correct
Great Work!
Incorrect
Vertical translations (shifts) of functions are written in the form `y=f(x)+color(royalblue)(c)`.`color(royalblue)(c)` is how many units up or down the graph will be shifted.`(-c) \ bb(darr)` Shift Down`(+c) \ bb(uarr)` Shift UpFor the equation: `y=f(x)color(royalblue)(-3)`, the value of `color(royalblue)(c)` is negative which means we translate (shift) the graph down by `color(royalblue)(3)` units.Use a table of values to find at least four points on the function `y=f(x)`.`x` `-9` `-5` `-1` `3` `6` `y` `0` `-3` `0` `5` `6` Sketch the graph of `y=f(x)` using the table of values.Since `c` is negative for `y=f(x)color(royalblue)(-3)` we will translate the graph down by `color(royalblue)(3)` units.
Sketch the graph of `y=f(x)-3` 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=1/x`
Which of the following is the graph of `y=1/x+2`?
Correct
Great Work!
Incorrect
Vertical translations (shifts) of functions are written in the form `y=f(x)+color(royalblue)(c)`.`color(royalblue)(c)` is how many units up or down the graph will be shifted.`(-c) \ bb(darr)` Shift Down`(+c) \ bb(uarr)` Shift UpFor the equation: `y=1/x color(royalblue)(+2)`, the value of `color(royalblue)(c)` is positive which means we translate (shift) the graph up by `color(royalblue)(2)` units.Use a table of values to find at least four points on the function `y=1/x`.`x` `-9` `-1` `1` `9` `y` `-1/9` `-1` `1` `1/9` Sketch the graph of `y=1/x` using the table of values.Since `c` is positive for `y=1/x color(royalblue)(+2)` we will translate the graph up by `color(royalblue)(2)` units.
Sketch the graph of `y=1/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=x^2`
Which of the following is the graph of `y=x^2 + 1`?
Correct
Great Work!
Incorrect
Vertical translations (shifts) of functions are written in the form `y=f(x)+color(royalblue)(c)`.`color(royalblue)(c)` is how many units up or down the graph will be shifted.`(-c) \ bb(darr)` Shift Down`(+c) \ bb(uarr)` Shift UpFor the equation: `y=x^2color(royalblue)(+1)`, the value of `color(royalblue)(c)` is positive which means we translate (shift) the graph up by `color(royalblue)(1)` units.Use a table of values to find at least four points on the function `y=x^2`.`x` `-2` `-1` `0` `1` `2` `y` `4` `1` `0` `1` `4` Sketch the graph of `y=x^2` using the table of values.Since `c` is positive for `y=x^2color(royalblue)(+1)` we will translate the graph up by `color(royalblue)(1)` units.
Sketch the graph of `y=x^2 + 1` 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^2`
Which of the following is the graph of `y=-x^2 + 4`?
Correct
Great Work!
Incorrect
Vertical translations (shifts) of functions are written in the form `y=f(x)+color(royalblue)(c)`.`color(royalblue)(c)` is how many units up or down the graph will be shifted.`(-c) \ bb(darr)` Shift Down`(+c) \ bb(uarr)` Shift UpFor the equation: `y=-x^2color(royalblue)(+4)`, the value of `color(royalblue)(c)` is positive which means we translate (shift) the graph up by `color(royalblue)(4)` units.Use a table of values to find at least four points on the function `y=-x^2`.`x` `-2` `-1` `0` `1` `2` `y` `-4` `-1` `0` `-1` `-4` Sketch the graph of `y=-x^2` using the table of values.
Since `c` is positive for `y=x^2color(royalblue)(+4)` we will translate the graph up by `color(royalblue)(4)` units.
Sketch the graph of `y=-x^2 + 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|`
Which of the following is the graph of `y=|x| + 2`?
Correct
Great Work!
Incorrect
Vertical translations (shifts) of functions are written in the form `y=f(x)+color(royalblue)(c)`.`color(royalblue)(c)` is how many units up or down the graph will be shifted.`(-c) \ bb(darr)` Shift Down`(+c) \ bb(uarr)` Shift UpFor the equation: `y=|x|color(royalblue)(+2)`, the value of `color(royalblue)(c)` is positive which means we translate (shift) the graph up by `color(royalblue)(2)` units.Use a table of values to find at least four points on the function `y=|x|`.`x` `-2` `-1` `0` `1` `2` `y` `2` `1` `0` `1` `2` Sketch the graph of `y=|x|` using the table of values.Since `c` is positive for `y=|x|color(royalblue)(+2)` we will translate the graph up by `color(royalblue)(2)` units.
Sketch the graph of `y=|x| + 2` 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=x^3`
Which of the following is the graph of `y=x^3` translated (shifted) up `3` units.
Correct
Great Work!
Incorrect
Vertical translations (shifts) of functions are written in the form `y=f(x)+color(royalblue)(c)`.`color(royalblue)(c)` is how many units up or down the graph will be shifted.`(-c) \ bb(darr)` Shift Down`(+c) \ bb(uarr)` Shift UpFor the equation: `y=x^3color(royalblue)(+3)`, the value of `color(royalblue)(c)` is positive which means we translate (shift) the graph up by `color(royalblue)(3)` 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 `c` is positive for `y=x^3color(royalblue)(+3)` we will translate the graph up by `color(royalblue)(3)` units.
Sketch the graph of `y=x^3 + 3` 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=\sqrt(x)`
Which of the following is the graph of `y=\sqrt(x) – 2`?
Correct
Great Work!
Incorrect
Vertical translations (shifts) of functions are written in the form `y=f(x)+color(royalblue)(c)`.`color(royalblue)(c)` is how many units up or down the graph will be shifted.`(-c) \ bb(darr)` Shift Down`(+c) \ bb(uarr)` Shift UpFor the equation: `y=\sqrt(x) color(royalblue)(-2)`, the value of `color(royalblue)(c)` is negative which means we translate (shift) the graph down by `color(royalblue)(2)` units.Use a table of values to find at least four points on the function `y=\sqrt(x)`.`x` `0` `1` `2` `3` `4` `y` `0` `1` `1.4` `1.7` `2` Sketch the graph of `y=\sqrt(x)` using the table of values.Since `c` is negative for `y = \sqrt(x) color(royalblue)(-2)` we will translate the graph down by `color(royalblue)(2)` units.
Sketch the graph of `y=\sqrt(x) – 2` 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