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Transformations of Functions>
Vertical Translations (Shifts)>
Vertical Translations (Shifts) 2Vertical Translations (Shifts) 2
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Question 1 of 7
1. Question
The graph below is `y=f(x)`
Sketch `y=f(x)-6`
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)(-6)`, the value of `color(royalblue)(c)` is negative which means we translate (shift) the graph down by `color(royalblue)(6)` units.Use a table of values to find at least four points on the function `y=f(x)`.`x` `-9` `-4` `0` `4` `6` `9` `y` `0` `4` `0` `5` `6` `6` Sketch the graph of `y=f(x)` using the table of values.Since `c` is negative for `y=f(x) color(royalblue)(-6)` we will translate the graph down by `color(royalblue)(6)` units.
Sketch the graph of `y=f(x)-6` 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-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=2^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=2^x`.`x` `-9` `0` `2` `3` `y` `0.002` `1` `4` `8` Sketch the graph of `y=2^x` using the table of values.Since `c` is negative for `y=2^x color(royalblue)(-3)` we will translate the graph down by `color(royalblue)(3)` units.
Sketch the graph of `y=2^x – 3` 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 – 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^2 color(royalblue)(-4)`, the value of `color(royalblue)(c)` is negative which means we translate (shift) the graph down 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 negative for `y=x^2 color(royalblue)(-4)` we will translate the graph down 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 4 of 7
4. Question
Given the parent function `y=x^2`
Which of the following is the graph of `y=x^2 – 6`?
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^2 color(royalblue)(-6)`, the value of `color(royalblue)(c)` is negative which means we translate (shift) the graph down by `color(royalblue)(6)` 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 negative for `y=x^2 color(royalblue)(-6)` we will translate the graph down by `color(royalblue)(6)` units.
Sketch the graph of `y=x^2-6` 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^2`
Which of the following is the graph of `y=-x^2 – 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^2 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=-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 negative for `y=-x^2 color(royalblue)(-2)` we will translate the graph down by `color(royalblue)(2)` units.
Sketch the graph of `y=-x^2 – 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=1/x`
Which of the following is the graph of `y=1/x` translated (shifted) `1` unit down?
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)(-1)`, the value of `color(royalblue)(c)` is negative which means we translate (shift) the graph down by `color(royalblue)(1)` unit.Use a table of values to find at least four points on the function `y=1/x`.`x` `-2` `-1` `1` `2` `3` `4` `y` `-1/2` `-1` `1` `1/2` `1/3` `1/4` Sketch the graph of `y=1/x` using the table of values.
Since `c` is negative for `y=1/x color(royalblue)(-1)` we will translate the graph down by `color(royalblue)(1)` unit.Use a table of values to find at least four points on the new function `y=1/x – 1` by shifting the `y`-values from the points on the original graph down by `color(royalblue)(1)` unit.`x` `-2` `-1` `1` `2` `3` `4` `y` `-3/2` `-2` `0` `-1/2` `-2/3` `-3/4` Plot the points for the new graph using the table of values.
Sketch the graph of `y=1/x – 1` 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=ln x`
Which of the following is the graph of `y=lnx + 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=lnx 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=lnx`.`x` `1/2` `1` `2` `3` `4` `y` `-0.7` `0` `0.7` `1.1` `1.4` Sketch the graph of `y=lnx` using the table of values.Since `c` is positive for `y=ln xcolor(royalblue)(+2)` we will translate the graph up by `color(royalblue)(2)` units.Use a table of values to find at least four points on the new function `y=lnx + 2` by shifting the `y`-values from the points on the original graph up by `color(royalblue)(2)` units.`x` `1/2` `1` `2` `3` `4` `y` `1.3` `2` `2.7` `3.1` `3.4` Plot the points for the new graph using the table of values.
Sketch the graph of `y=lnx + 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