Graphing Reflections 2
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Question 1 of 5
1. Question
Given `x^2 +(y+2)^2 =9`
Reflect `x^2 +(y+2)^2 =9` across the
`x`-axisCorrect
Great Work!
Incorrect
Reflections around the `x`-axis have the property `\ \ y=-f(x)`.Replace `y\rightarrow-y`.To sketch `x^2 +(-y+2)^2 =9`, we first look at the graph of `x^2 +(y+2)^2 =9`.Since the standard form of the equation of a circle is `(x-h)^2 + (y-k)^2 = r^2`, we know that the center of the circle is `(h,k)` and the radius is `r`.From the equation of the original function `x^2 +(y+2)^2 =9`, the center of the circle is `(0,-2)` and the radius is `r=\sqrt(9)=3`.Sketch the graph of the original function `x^2 +(y+2)^2 =9` using the center and the radius.
Reflect across the `x`-axis by replacing `y` for `-y`, therefore `x^2+(-y+2)^2=9.` Which is the same as
`x^2+(y-2)^2=9.`
Sketch the graph of `x^2 +(-y+2)^2 =9` by following the shape and radius of the original graph.
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Question 2 of 5
2. Question
Given `y=f(x)`
Sketch `y=f(-x)`
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Question 3 of 5
3. Question
Given `y=f(x)`
Sketch `y=-f(-x)`
Correct
Great Work!
Incorrect
Reflections around the `y`-axis have the property`\ \ y=f(-x)`.Replace `x\rightarrow-x`.Reflections around the `x`-axis have the property `\ \ y=-f(x)`Replace `y\rightarrow-y`.To sketch `y=-f(-x)`, we first look at the graph of `y=f(x)`.Use a table of values to find at least four points on the function `y=f(x)`.`x` `-4` `0` `4` `8` `9` `y` `4` `0` `4` `0` `-3` Sketch the graph of `y=f(x)` using the table of values.Reflect the points marked for `y=f(x)` across the `x`-axis.
`y=-f(-x)` consists of one reflection about the x-axis and then one reflection about the y-axis.
This is exactly the same as a `180°` rotation about the origin.
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Question 4 of 5
4. Question
Given `y=f(x)`
Sketch `y=-f(x)`
Correct
Great Work!
Incorrect
Reflections around the `x`-axis have the property `\ \ y=-f(x)`.Replace `y\rightarrow-y`.To sketch `y=-f(x)`, we first look at the graph of `y=f(x)`.Use a table of values to find at least four points on the function `y=f(x)`.`x` `3` `3` `7` `9` `y` `6` `-4` `0` `-2` Sketch the graph of `y=f(x)` using the table of values.
Reflect the points marked for `y=f(x)` across the `x`-axis.
Sketch the graph of `y=-f(x)` by following the shape of the original graph but connecting the new translated points.
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Question 5 of 5
5. Question
Given `f(x)=1/(x-3)`
Sketch the graph of `y=f(-x)`
Correct
Great Work!
Incorrect
Reflections around the `y`-axis have the property `\ \ y=f(-x)`.Replace `x\rightarrow-x`.To sketch the transformed function `y=f(-x)`, start by sketching the original function `f(x)=1/(x-3)`.Find the asymptotes of the function `f(x)=1/(x-3)`.`x-3=` `0` Set the denominator `x-3` equal to `0`. `x=` `3` Add `3` to both sides of the equation. Then, sketch the original function `f(x)=1/(x-3)` by using the Asymptote`x=3`. Remember that this function is a hyperbola.
Now sketch the transformed function `y=f(-x)` which is `f(x)=1/(-x-3)=-1/(x+3)`.Find the asymptotes of the function `f(x)=-1/(x+3)`.`x+3=` `0` Set the denominator `x+3` equal to `0`. `x=` `-3` Subtract `3` to both sides of the equation. Sketch the transformed function `f(x)=-1/(x+3)` by using the Asymptote`x=-3`. Remember that this function is a hyperbola.
Quizzes
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- Vertical Translations 2
- Vertical Translations from a Point
- Horizontal Translations 1
- Horizontal Translations 2
- Horizontal Translations from a Point
- Horizontal Translations from a Graph
- Horizontal and Vertical Translations from a Graph
- Sketch a Graph using Translations
- Write the Equation from a Graph
- Write the Equation from Translations
- Vertical Dilations
- Horizontal Dilations 1
- Horizontal Dilations 2
- Horizontal Dilations – Scale Factor
- Horizontal and Vertical Dilations 1
- Horizontal and Vertical Dilations 2
- Horizontal and Vertical Dilations 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