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Sketch a Graph using Translations>
Sketch a Graph using TranslationsSketch a Graph using Translations
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Question 1 of 4
1. Question
Sketch the graph for `y=1/(x+2) + 3` by using `y=1/x`.
Correct
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Incorrect
Horizontal and vertical translations of cubed functions are written in the form `y=1/(x-h) + c` where the point `(h,c)` is the intersection point of the asymptotes.To sketch the graph of `y=1/(x+2) + 3`, first find the intersection of the asymptotes and generate a table of values.The formula `y=1/(x-h) + c` when applied to `y=1/x` (can be rewritten as `y=1/(x-(0)) + 0`) gives the intersection point of the asymptotes at `(-2,3)`.Generate a table of values for `y=-x^3` with at least four points.`x` `-2` `-1` `0` `1` `2` `y` `-1/2` `-1` `x` `1` `1/2` Sketch the function `y=1/x` using the table of values and the intersection point of the asymptotes.
Using the formula `y=1/(x-h) + c` for horizontal and vertical translations and remembering that the point `(h,c)` is the intersection point of the asymptotes, the intersection point of the asymptotes for `y=1/(x+2) + 3` is `(-2,3)`.
Sketch the curve for `y=1/(x+2) + 3` through the intersection point of its asymptotes `(-2,3)` following the same shape as `y=1/x`.
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Question 2 of 4
2. Question
Sketch the graph for `y=\sqrt(x+3)-2` by using `y=\sqrt(x)`.
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Horizontal and vertical translations of cubed functions are written in the form `y=\sqrt(x-h)+c` where the point `(h,c)` is the vertex of the function.To sketch the graph of `y=\sqrt(x+3)-2`, first find the vertex and generate a table of values.The formula `y=\sqrt(x-h)+c` when applied to `y=\sqrt(x)` (can be rewritten as `y=\sqrt(x-0)+0`) gives the vertex at `(0,0)`.Generate a table of values for `y=1/x` with at least four points.`x` `0` `1` `2` `4` `6` `y` `0` `1` `1.4` `2` `2.4` Sketch the function `y=1/x` using the table of values and the vertex point.
Using the formula `y=\sqrt(x-h)+c` for horizontal and vertical translations and remembering that the point `(h,c)` is the vertex of the function, the vertex point for `y=\sqrt(x+3)-2` is `(-3,-2)`.
Sketch the curve for `y=\sqrt(x+3)-2` through its vertex point `(-3,-2)` following the same shape as `y=\sqrt(x)`.
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Question 3 of 4
3. Question
Sketch the graph for `y=(x -2)^3 – 1` by using `y=x^3`.
Correct
Great Work!
Incorrect
Horizontal and vertical translations of cubed functions are written in the form `y=(x-h)^3 +c` where the point `(h,c)` is the vertex of the function.To sketch the graph of `y=(x -2)^3-1`, first find the vertex and generate a table of values.The formula `y=(x-h)^3 +c` when applied to `y=x^3` (can be rewritten as `y=(x-0)^3+0`) gives the vertex at `(0,0)`.Generate a table of values for `y=-x^3` with at least four points.`x` `-2` `-1` `0` `1` `2` `y` `-8` `-1` `0` `1` `8` Sketch the function `y=x^3` using the table of values and the vertex point.
Using the formula `y=(x-h)^3 +c` for horizontal and vertical translations and remembering that the point `(h,c)` is the vertex of the function, the vertex point for `y=(x -2)^3-1` is `(2,-1)`.
Sketch the curve for `y=(x -2)^3-1` through its vertex point `(2,-1)` following the same shape as `y=x^3`.
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Question 4 of 4
4. Question
Sketch the graph for `y=2^(x-1) -2` by using `y=2^x`.
Correct
Great Work!
Incorrect
Horizontal and vertical translations of cubed functions are written in the form `y=2^(x-h) +c` where `y=c` is the asymptote of the function.To sketch the graph of `y=2^(x -1)-2`, first find the asymptote and generate a table of values.The formula `y=2^(x-h) +c` when applied to `y=2^x` (can be rewritten as `2^(x-0) +0`) gives the asymptote at `y=0`.Generate a table of values for `y=2^x` with at least four points.`x` `-2` `0` `1` `2` `3` `y` `1/4` `1` `2` `4` `8` Sketch the function `y=2^x` using the table of values and the asymptote.
Using the formula `y=2^(x-h) +c` for horizontal and vertical translations and remembering that the point `y=c` is the equation of the asymptote of the function, the asymptote for `y=2^(x -1)-2` is `y=-2`.
Sketch the curve for `y=2^(x -1)-2` following its asymptote `y=-2` following the same shape as `y=2^x`.
Quizzes
- Vertical Translations 1
- 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