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Write the Equation from a GraphWrite the Equation from a Graph
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Question 1 of 2
1. Question
Find the equation of the function below by using the graph for `y=x^3`.
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Horizontal and vertical translations of cubic functions are written in the form `y=(xcolor(red)(h))^3 + color(blue)(c)` where the point `(color(red)(h),color(blue)(c))` is the vertex of the function.`color(red)(h)` is a shift to the right and `color(blue)(+c)` is a shift upwards.`(h) \ bb(rarr)` Shift Right`(+h) \ bb(larr)` Shift Left`(c) \ bb(darr)` Shift Down`(+c) \ bb(uarr)` Shift UpTo obtain the equation of the function by using the graph for `y=x^3`, first sketch the function `y=x^3`.Sketch the function `y=x^3`. Remember the formula `y=(xcolor(red)(h))^3 + color(blue)(c)` when applied to `y=x^3` (can be rewritten as `y=(xcolor(red)(0))^3+color(blue)(0)`) has its vertex at `(color(red)(0),color(blue)(0))`.To find the horizontal shift (`h`), count the units between the graphs along the `x`axis. It is `3` units to the right (`h=3`).To find the vertical shift (`c`), count the units between the graphs along the `y`axis. It is `1` unit down (`c=1`).Put the equation together using the formula `y=(xcolor(red)(h))^3 + color(blue)(c)`, `color(red)(h=3)`, and `color(blue)(c=1)`. The unknown graph is `y=(xcolor(red)(3))^3 color(blue)(1)`.`y=(x3)^3 1` 
Question 2 of 2
2. Question
Find the equation of the function below by using the graph for `y=1/x`.
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Horizontal and vertical translations of hyperbolic functions are written in the form `y=1/(xcolor(red)(h)) +color(blue)(c)` where the point `(color(red)(h),color(blue)(c))` is the intersection point of the asymptotes of the function.`color(red)(h)` is a shift to the right and `color(blue)(+c)` is a shift upwards.`(h) \ bb(rarr)` Shift Right`(+h) \ bb(larr)` Shift Left`(c) \ bb(darr)` Shift Down`(+c) \ bb(uarr)` Shift UpTo obtain the equation of the function by using the graph for `y=1/x`, first sketch the function `y=1/x`.Sketch the function `y=1/x`. Remember the formula `y=1/(xcolor(red)(h)) +color(blue)(c)` when applied to `y=1/x` (can be rewritten as `y=1/(xcolor(red)(0))+color(blue)(0)`) has the intersection point of the asymptotes at `(color(red)(0),color(blue)(0))`.To find the horizontal shift (`h`), count the units between the graphs along the `x`axis. It is `2` units to the right (`h=2`).To find the vertical shift (`c`), count the units between the graphs along the `y`axis. It is `3` units up (`c=3`).Put the equation together using the formula `y=1/(xcolor(red)(h)) +color(blue)(c)`, `color(red)(h=2)`, and `color(blue)(c=3)`. The unknown graph is `y=1/(xcolor(red)(2))+color(blue)(3)`.`y=1/(x2)+3`
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