Vertical dilation takes the form y=kf(x) where k is the vertical scale factor.
Horizontal dilation takes the form y=f(ax) where the scale factor can be found from xFactor or Factor=1a .
To find which type of dilation (stretch/shrink) is happening, compare the transformed function y=1(4x)+6 to the vertical dilation form y=kf(x) and the horizontal dilation form y=f(ax).
The transformed function y=1(4x)+6 looks like the horizontal dilation form y=f(ax). This means that a=4.
Calculate the horizontal scale factor by using Factor=1a and a=4.
Factor=
14
Simplify
Factor=
14
Horizontal dilation with a scale factor of 14
Question 4 of 6
4. Question
What is the equation when y=x2+5 is vertically dilated (stretch/shrink) by a factor of -1.
Vertical dilation takes the form y=kf(x) where k is the vertical scale factor.
Horizontal dilation takes the form y=f(ax) where the scale factor can be found from xFactor or Factor=1a .
Since the dilation (stretch/shrink) is vertical with a factor of -1, we follow the vertical dilation form y=(k)f(x). Remember that k is the scale factor.
So, we can say the k=-1.
From there, the original function y=x2+5 will become y=-1(x2+5) or simply y=-x2-5.
y=-x2-5
Question 5 of 6
5. Question
What is the equation when x2+y2=25 is vertically dilated (stretch/shrink) by a factor of 14.
Vertical dilation takes the form y=kf(x) where k is the vertical scale factor.
Horizontal dilation takes the form y=f(ax) where the scale factor can be found from xFactor or Factor=1a .
Since the dilation (stretch/shrink) is vertical with a factor of 14, we follow the vertical dilation form y=(k)f(x). Remember that k is the scale factor.
So, we can say the k=14.
From there, the original function x2+(y14)2=25 will become x2+(4y)2=25 or simply x2+16y2=25.
x2+16y2=25
Question 6 of 6
6. Question
What dilation (stretch/shrink) is needed to transform y=x3+6x to y=18x3+3x?
Vertical dilation takes the form y=kf(x) where k is the vertical scale factor.
Horizontal dilation takes the form y=f(ax) where the scale factor can be found from xFactor or Factor=1a .
To find which type of dilation (stretch/shrink) is happening, compare the transformed function y=18x3+3x to the vertical dilation form y=kf(x) and the horizontal dilation form y=f(ax).
The transformed function y=18x3+3x looks like the horizontal dilation form y=f(ax). This means that a=36 or simply a=12.
Calculate the horizontal scale factor by using Factor=1a and a=12.