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.
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)
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.
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=-1
y=
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
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.
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=y13
x2+(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
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.
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.