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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=(x-color(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=(x-color(red)(h))^3 + color(blue)(c)` when applied to `y=x^3` (can be rewritten as `y=(x-color(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=(x-color(red)(h))^3 + color(blue)(c)`, `color(red)(h=3)`, and `color(blue)(c=-1)`. The unknown graph is `y=(x-color(red)(3))^3 color(blue)(-1)`.
`y=(x-3)^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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Great Work!
Incorrect
Horizontal and vertical translations of hyperbolic functions are written in the form `y=1/(x-color(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/(x-color(red)(h)) +color(blue)(c)` when applied to `y=1/x` (can be rewritten as `y=1/(x-color(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/(x-color(red)(h)) +color(blue)(c)`, `color(red)(h=2)`, and `color(blue)(c=3)`. The unknown graph is `y=1/(x-color(red)(2))+color(blue)(3)`.
`y=1/(x-2)+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