Topics
>
Precalculus>
Transformations of Functions>
Combinations of Transformations: Find Equation>
Combinations of Transformations: Find Equation 2Combinations of Transformations: Find Equation 2
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 6 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
- 6
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- 6
- Answered
- Review
-
Question 1 of 6
1. Question
Find the transformed version of `y=1/x` when a horizontal translation of `3` units left, a vertical dilation of `2`, and a vertical translation of `4` units down are applied.
Correct
Great Work!
Incorrect
A standard function form for a horizontal translation is `y=f(x+color(red)(h))` where `color(red)(+h)` is a shift to the left movement along the `x`-axis.A standard function form for a vertical translation is `y=f(x)+color(purple)(c)` where `color(purple)(+c)` is an upward movement along the `y`-axis.A standard function form for a vertical dilation is `color(blue)(k)f(x)` where `color(blue)(k)` is the vertical dilation factor.To transform `y=1/x` with a horizontal translation of `color(red)(3)` units left, a vertical dilation of `color(blue)(2)`, and a vertical translation of `color(purple)(4)` units down, first apply a horizontal translation moving to the left (negative) which means that `color(red)(+h)` is a positive. Do this by using `y=f(x+color(red)(h))` and `color(red)(h=3)`.`y=` `1/x` Apply the horizontal translation of `color(red)(h=3)`. Remember `y=f(x+color(red)(h))`. `=` `1/(xcolor(red)(+3))` Simplify `=` `1/(x+3)` Now apply the vertical dilation of `color(blue)(k=2)`. Use `color(blue)(k)f(x)`.`y=` `1/(x+3)` Apply the vertical dilation of `color(blue)(k=2)`. Use `color(blue)(k)f(x)`. `=` `color(blue)(2)times(1/(x+3))` Simplify `=` `2/(x+3)` Finally apply the vertical translation of `color(purple)(4)` units down. Use `y=f(x)+color(purple)(c)` where `color(purple)(c)` is an upward movement along the `y`-axis. In this case `color(purple)(c=-4)` because we are going downward.`y=` `2/(x+3)` Apply the vertical translation of `color(purple)(4)` units down. This means `color(purple)(c=-4)`. `=` `2/(x+3)color(purple)(-4)` Simplify `=` `2/(x+3)-4` `y=2/(x+3)-4` -
Question 2 of 6
2. Question
Find the equation when `y=x^3` is transformed with a horizontal dilation factor of `2` then a vertical translation of `3` units up.
Correct
Great Work!
Incorrect
The application of the horizontal dilation (`color(blue)(text{factor})`) on a `x` variable is `x/color(blue)(text{factor})`.A standard function form for a vertical translation is `y=f(x)+color(purple)(c)` where `color(purple)(c)` is an upward movement along the `y`-axis.To determine the transformed equation, start by applying the horizontal dilation factor of `color(blue)(2)` first. Do this by using `x/color(blue)(text{factor})` and `color(blue)(text{factor})color(blue)(=2)`.`y=` `x^3` Apply the horizontal dilation factor of `color(blue)(2)`. Remember `x/color(blue)(text{factor})`. `=` `(x/{color(blue)(2)})^3 ` Simplify `=` `(x/2)^3` Apply the vertical translation of `color(purple)(3)` units up. Use `y=f(x)+color(purple)(c)` where `color(purple)(c)` is an upward movement along the `y`-axis. This means `color(purple)(c=3)`. `=` `(x/2)^3 color(purple)(+3)` Simplify `=` `(x/2)^3 +3` Simplify. `y=` `x^3/8 +3` Simplify. `y=x^3/8 +3` -
Question 3 of 6
3. Question
Find the equation when `y=sqrt(x)` is reflected about the `y`-axis then transformed with a vertical dilation factor of `2`, then a horizontal dilation factor of `1/3`.
Correct
Great Work!
Incorrect
Reflections about the `y`-axis have the property where we replace `x\rightarrow-x`.
A standard function form for a vertical dilation is `color(blue)(k)f(x)` where `color(blue)(k)` is the vertical dilation.
The application of the horizontal dilation (`color(green)(text{factor})`) on a `x` variable is `x/color(green)(text{factor})`.To determine the transformed equation, start by applying the reflection around the `y`-axis by replacing `x\rightarrow-x`.`y=` `sqrt(-x)` Replace `x` by `-x`. `=` `color(blue)(2)sqrt(-x)` Apply the vertical dilation of `color(blue)(k=2)`. Use `color(blue)(k)f(x)`. `=` `2sqrt(-x)` Apply the horizontal dilation factor of `color(green)(1/3)`. Remember `x/color(green)(text{factor})` `=` `2sqrt(-x/color(green)(1/3))` Simplify `y=` `2sqrt(-3x)` `y=2sqrt(-3x)` -
Question 4 of 6
4. Question
Find the transformed equation when the original function `y=logx` is translated horizontally by `2` units to the right, then transformed with the horizontal dilation factor of `3`.
Correct
Great Work!
Incorrect
A standard function form for a horizontal translation is `y=f(x+color(red)(h))` where `color(red)(+h)` is a shift to the left movement along the `x`-axis.The application of the horizontal dilation (`color(blue)(text{factor})`) on a `x` variable is `x/color(blue)(text{factor})`.To determine the transformed equation, we start by applying the horizontal translation of `color(red)(2)` units right. Use `y=f(x+color(red)(h))` where `color(red)(h)` is a shift to the left along the `x`-axis. This means `color(red)(h=-2)`.`y=` `logx` Apply the horizontal translation of `color(red)(2)` units right. Use `y=f(xcolor(red)(-2))`. `=` `log(xcolor(red)(-2))` Simplify `=` `log(x-2)` Apply the horizontal dilation factor of `color(blue)(3)`. Remember `x/color(blue)(text{factor})`. `=` `log((x/color(blue)(3)) -2)` Simplify `y=` `log(1/3x – 2)` `y=log(1/3x – 2)` -
Question 5 of 6
5. Question
Find the transformed version of `y=3^x` when a vertical translation of `2` units up, a horizontal translation of `2` units to the right, and a vertical dilation factor of `-1` are applied.
Correct
Great Work!
Incorrect
A standard function form for a horizontal translation is `y=f(x+color(red)(h))` where `color(red)(+h)` is a shift to the left movement along the `x`-axis.A standard function form for a vertical translation is `y=f(x)+color(purple)(c)` where `color(purple)(+c)` is an upward movement along the `y`-axis.A standard function form for a vertical dilation is `color(blue)(k)f(x)` where `color(blue)(k)` is the vertical dilation.To transform `y=3^x` with a vertical translation of `color(purple)(2)` units up, horizontal translation of `color(red)(2)` units right, and a vertical dilation of `color(blue)(-1)`, first apply a vertical translation of `2` units up. This means `color(purple)(c=2)`.`y=` `3^x` Apply the vertical translation of `color(purple)(2)` units up. Use `y=f(x)+color(purple)(c)` where `color(purple)(+c)` is an upward movement along the `y`-axis. This means `color(purple)(c=2)`. `=` `3^x + color(purple)(2)` Simplify `=` `3^x + 2` Next, remember `color(red)(+h)` (left) is a shift to the left along the `x`-axis. So moving to the right, `color(red)(h)` is a negative. Do this by using `y=f(x+color(red)(h))` and `color(red)(h=-2)`.`y=` `3^x + 2` Apply the horizontal translation of `color(red)(h=-2)`. Remember `y=f(x+color(red)(h))`. `=` `3^(xcolor(red)(-2)) + 2` Simplify `=` `3^(x-2) + 2` Now apply the vertical dilation of `color(blue)(k=-1)`. Use `color(blue)(k)f(x)`.`y=` `3^(x-2) + 2` Apply the vertical dilation of `color(blue)(k=-1)`. Use `color(blue)(k)f(x)`. `=` `color(blue)(-1)[3^(x-2) + 2]` Simplify `=` `-3^(x-2) – 2` `y=-3^(x-2) – 2` -
Question 6 of 6
6. Question
Find the equation when `y=sqrt(x)` is transformed with a vertical translation of `3` units up, a horizontal dilation factor of `2`, a horizontal translation of `1` unit up, and a reflection about the `x`-axis.
Correct
Great Work!
Incorrect
A standard function form for a horizontal translation is `y=f(x+color(red)(h))` where `color(red)(+h)` is a shift to the left movement along the `x`-axis.A standard function form for a vertical translation is `y=f(x)+color(purple)(c)` where `color(purple)(+c)` is an upward movement along the `y`-axis.The application of the horizontal dilation `color(blue)(text{factor})` on a `x` variable is `x/color(blue)(text{factor})`.Reflections about the `x`-axis have the property where we replace `y\rightarrow-y`.To determine the transformed equation, start by applying the vertical translation of `color(purple)(3)` units up. Use `y=f(x)+color(purple)(c)` where `color(purple)(+c)` is an upward movement along the `y`-axis. This means `color(purple)(c=3)` .`y=` `sqrt(x)color(purple)(+3)` Apply the vertical translation `color(purple)(c=3)`. `=` `sqrt(x/color(blue)(2))+3` Apply the horizontal dilation factor of `color(blue)(2)`. Remember `x/color(blue)(text{factor})`. `=` `sqrt(1/2(xcolor(red)(-1)))+3` Apply the horizontal translation `color(red)(-1)` unit right. `=` `-[sqrt(1/2(x-1))+3]` Reflecting about the `x`-axis. Replace `y` for `-y`. `y=` `-sqrt(1/2(x-1))-3` `y=-sqrt(1/2(x-1))-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