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Transformations of Functions>
Combinations of Transformations: Find Equation>
Combinations of Transformations: Find Equation 3Combinations of Transformations: Find Equation 3
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Question 1 of 6
1. Question
Find the transformed version of y=x4 when a horizontal dilation factor of 13 and a vertical translation of 6 units up are applied.
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A standard function form for a vertical translation is y=f(x)+c where +c is an upward movement along the y-axis.The application of the horizontal dilation factor on a x variable is xfactor.To transform y=x4 with a horizontal dilation factor of 13 and a vertical translation of 6 units up, start by applying the horizontal dilation factor. Do this by using xfactor and factor=13.y= x4 Apply the horizontal dilation factor of 13. Remember xfactor. = (x13)4 Simplify = (3x)4 = 81x4 Now apply the vertical translation of 6 units up. Use y=f(x)+c where +c is an upward movement along the y-axis. This means c=6.y= 81x4 Apply the vertical translation of 6 units up. Use y=f(x)+c where c is an upward movement along the y-axis. This means c=6. = 81x4+6 Simplify = 81x4+6 y=81x4+6 -
Question 2 of 6
2. Question
Find the equation when y=lnx is transformed with a horizontal dilation factor of 5 then a vertical translation of 2 units down.
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A standard function form for a vertical translation is y=f(x)+c where +c is an upward movement along the y-axis.The application of the horizontal dilation factor on a x variable is xfactor.To determine the transformed equation, start by applying the horizontal dilation factor of 5 first. Do this by using xfactor and factor=5.y= lnx Apply the horizontal dilation factor of 5. Remember xfactor. = ln(x5) Simplify = ln(x5) Apply the vertical translation of 2 units down. Use y=f(x)+c where +c is an upward movement along the y-axis. This means c=-2. = ln(x5)-2 Simplify y= ln(x5)-2 y=ln(x5)-2 -
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Question 3 of 6
3. Question
Find the equation when y=logx is transformed with a vertical dilation factor of 4 then a horizontal dilation factor of 12.
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A standard function form for a vertical dilation is kf(x) where k is the vertical dilation. The application of the horizontal dilation factor (factor) on a x variable is xfactor.To determine the transformed equation, start by applying the vertical dilation factor of 4 first.y= logx Apply the vertical dilation of k=4. Use kf(x). = 4logx Apply the horizontal dilation factor of 12. Remember xfactor = 4log(x12) Simplify y= 4log(2x) y=4log(2x) -
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Question 4 of 6
4. Question
Find the transformed version of y=x2 when a vertical translation of 2 units up, a horizontal dilation of 4 units to the left, and a horizontal translation of 1 unit right are applied.
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A standard function form for a horizontal translation is y=f(x+h) where +h is a shift to the left movement along the x-axis.A standard function form for a vertical translation is y=f(x)+c where +c is an upward movement along the y-axis.The application of the horizontal dilation (factor) on a x variable is xfactor.To transform y=x2 when a vertical translation of 2 units up, a horizontal dilation of 4 and a horizontal translation of 1 unit right, start by applying the vertical translation. Use y=f(x)+c where c is an upward movement along the y-axis. This means c=2.y= x2 Apply the vertical translation of c=2. Remember y=f(x)+c. = x2+2 Simplify = x2+2 Now apply the horizontal dilation of 4. Do this by using xfactor and factor=4.y= x2+2 Apply the horizontal dilation of 4. Remember xfactor. = (x4)2+2 Simplify = x216+2 Finally apply the horizontal translation of 1 unit right. Do this by using y=f(x+h) and h=-1y= x216+2 Apply the horizontal translation of 1 unit right. Use y=f(x+h). In this case -h is a shift to the right along the x-axis. This means h=-1. = (x-1)216+2 Simplify = 116(x-1)2+2 y=116(x-1)2+2 -
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Question 5 of 6
5. Question
Find the equation if x2+y2=9 is shifted 3 units down and transformed with a vertical dilation factor of 13.
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A standard circle equation is in the form (x-h)2+(y-c)2=r2 where:- h is the x-coordinate of the vertex
- c is the y-coordinate of the vertex
Vertical Dilation factor is k, y=kf(x)โดyk=yfactor=f(x)First we start with a vertical translation of 3 units down.x2+y2= 9 Apply the vertical translation of 3 units down. Use c=-3. (x-h)2+(y-c)2= 9 (x-0)2+(y--3)2= 9 x2+(y+3)2= 9 Simplify x2+(y+3)2= 9 Now apply the vertical dilation factor of k=13. Use y=kf(x).yk is the same as yfactor=y13x2+(y+3)2= 9 Apply the vertical dilation factor k=13. x2+((yk=13)+3)2= 9 Simplify x2+(3y+3)2= 9 Factor 3. x2+9(y+1)2= 9 x2+9(y+1)2=9 -
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Question 6 of 6
6. Question
Find the transformed equation when the original function y=x2 is translated horizontally 4 units to the left, then transformed with the horizontal dilation factor of 14.
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Need TextPlayCurrent Time 0:00/Duration Time 0:00Remaining Time -0:00Stream TypeLIVELoaded: 0%Progress: 0%0:00Fullscreen00:00MutePlayback Rate1x- 2x
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Chapters- Chapters
A standard function form for a horizontal translation is y=f(x+h) where +h is a shift to the left along the x-axis. The application of the horizontal dilation (factor) on a x variable is xfactor.To determine the transformed equation, we start by applying the horizontal translation of 4 units left. Use y=f(x+h) where +h is a shift left along the x-axis. This means h=+4.y= x2 Apply the horizontal translation of +4 units left. Use y=f(x+4). = (x+4)2 Simplify = (x+4)2 Apply the horizontal dilation factor of 14. Remember xfactor. = (x14+4)2 Simplify y= (4x+4)2 Factor out 4. y= 16(x+1)2 y=16(x+1)2 -
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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 โ 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