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Reflection with Rotation>
Reflection with RotationReflection with Rotation
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Question 1 of 5
1. Question
Given `y=(x2)^2 1`.
Sketch `y=f(x)`
Correct
Great Work!
Incorrect
A rotation of `180` degrees (about the origin) is found when `y=f(x)` is transformed to `y=f(x)`.To be able to sketch the new function after the rotation of `180` degrees, find `y=f(x)`.`f(x)=` `(x2)^21` `f(x)=` `color(red)()[((color(blue)(x)2)^2 – 1]` Transform `y=f(x)` into `y=f(x)`. Simplify inside the square brackets first. `=` `color(red)()[(x+2)^2 – 1]` `=` `(x+2)^2 + 1` Set `(x+2)^2 + 1` equal to zero and solve for `x`. This will give you the rotated `x`intercepts.`(x+2)^2=` ` + 1` Adding `(x+2)^2` to both sides. `x+2=` `\pm 1` Taking the square root of both sides. `x=` `\pm 1 – 2` Subtracting `2`to both sides `x=` `1 – 2` For the positive `1`. `x=` `1` This is the first point. `x=` `1 – 2` For the negative `1`. `x=` `3` This is the second point. Now plot these `x`intercept points on the graph.Rotate `180°` and sketch the original graph around the point `(0,0)` and going through `x`intercept `x=1`, and `x`intercept `x=3`. 
Question 2 of 5
2. Question
Given `y=(x+1)^2`.
Sketch `y=f(x)`
Correct
Great Work!
Incorrect
A rotation of `180` degrees (about the origin) is found when `y=f(x)` is transformed to `y=f(x)`.To be able to sketch the new function after the rotation of `180` degrees, find `y=f(x)`.`f(x)=` `(x+1)^2` `f(x)=` `color(red)()[((color(blue)(x)+1)^2]` Transform `y=f(x)` into `y=f(x)`. Simplify inside the square brackets first. `=` `color(red)()[(x1)^2]` `=` `(x1)^2` Set `(x1)^2` equal to zero and solve for `x`. This will give you the rotated `x`intercepts.`(x1)^2=` `0` Multiplying both sides by `1`. `x1=` `0` Taking the square root of both sides. `x=` `1` Adding `1` to both sides. Now plot these `x`intercept points on the graph.Rotate `180°` and sketch the original graph around the point `(0,0)` and going through `x`intercept `x=1`. 
Question 3 of 5
3. Question
Given `y=x^3+2x^23x`.
Sketch `y=f(x)`
Correct
Great Work!
Incorrect
A rotation of `180` degrees (about the origin) is found when `y=f(x)` is transformed to `y=f(x)`.To be able to sketch the new function after the rotation of `180` degrees, find `y=f(x)`.Transform `y=f(x)` into `y=f(x)`. Simplify inside the square brackets first.`f(x)=` `x^3+2x^23x` `f(x)=` `color(red)()[(color(blue)(x))^3+2(color(blue)(x))^23(color(blue)(x))]` `=` `color(red)()[x^3+2x^2+3x]` `=` `x^32x^23x` Now factor `f(x)=x^32x^23x`.`f(x)=` `x^32x^23x` Remove an `x` from each term. `=` `x(x^22x3)` Factor inside the brackets `=` `x(x3)(x+1)` Set `x`, `x3`, and `x+1` equal to zero and solve for `x`. This will give you the rotated `x`intercepts.`x=` `0` This is the first point. `x3=` `0` This is the second point. Simplify. `x=` `3` `x+1=` `0` This is the third point. Simplify. `x=` `1` Now plot these `x`intercept points on the graph.Rotate `180°` and sketch the original graph around the point `(0,0)` and going through `x`intercept `x=0`, `x`intercept `x=3` and `x`intercept `x=1`. 
Question 4 of 5
4. Question
Rotate `y=sqrt(x)` by `180` degrees about the origin.
Correct
Great Work!
Incorrect
A rotation of `180` degrees (about the origin) is found when `y=f(x)` is transformed to `y=f(x)`.To be able to sketch the new function after the rotation of `180` degrees, find `y=f(x)`.`f(x)=` `sqrt(x)` `f(x)=` `color(red)() [sqrt(color(blue)(x)) ]` Transform `y=f(x)` into `y=f(x)`. Simplify inside the square brackets first. `=` `color(red)()[sqrt(x)]` `=` `sqrt(x)` Set `sqrt(x)` equal to zero and solve for `x`. This will give you the rotated `x`intercepts.`sqrt(x)=` `0` Take the square of both sides `x=` `0` Simplify. `x=` `0` Now plot this ‘ x’intercept point on the graph.Rotate `180°` and sketch the original graph around the point `(0,0)` and going through `x`intercept `x=0`. 
Question 5 of 5
5. Question
Given `y=(x1)^3`.
Sketch `y=f(x)`
Correct
Great Work!
Incorrect
A rotation of `180` degrees (about the origin) is found when `y=f(x)` is transformed to `y=f(x)`.To be able to sketch the new function after the rotation of `180` degrees, find `y=f(x)`.`f(x)=` `(x1)^3` `f(x)=` `color(red)()(color(blue)(x)1)^3` Transform `y=f(x)` into `y=f(x)`. `=` `(x1)^3` Set `(x1)^3` equal to zero and solve for `x`. This will give you the rotated `x`intercepts.`(x1)=` `0` Taking the cube root of both sides. `x+1=` `0` Distributing the negative sign `x=` `1` Now plot these `x`intercept points on the graph.Rotate `180°` and sketch the original graph around the point `(0,0)` and going through `x`intercept `x=1`.
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