Transformations of Functions

Question 1

What has happened to the function y=f(x) to make it y=3f(x)?

Answer 1

Stretch, scale factor 3, in the y-direction

Question 2

What has happened to the function y=f(x) to make it y=1/4f(x)?

Answer 2

Stretch, scale factor 1/4, in the y-direction

Question 3

What has happened to the function y=f(x) to make it y=f(2x)?

Answer 3

Stretch, scale factor 1/2, in the x-direction

Question 4

What has happened to the function y=f(x) to make it y=f(x)+4?

Answer 4

Translation, 4 units up in the y-direction

Question 5

What has happened to the function y=f(x) to make it y=f(x)-1?

Answer 5

Translation, 1 unit down in the y-direction

Question 6

If y=f(x) undergoes the this transformation, what is the new equation?Translation 1 unit in the positive y-direction

Answer 6

y=f(x)+1

Question 7

If y=f(x) undergoes the this transformation, what is the new equation?Translation 1 unit in the positive x-direction

Answer 7

y=f(x-1)

Question 8

If y=f(x) undergoes the this transformation, what is the new equation?Stretch parallel to the y-axis, scale factor 3

Answer 8

y=3f(x)

Question 9

If y=f(x) undergoes the this transformation, what is the new equation?Stretch parallel to the y-axis, scale factor 1/5

Answer 9

y=1/5f(x)

Question 10

If y=f(x) undergoes the this transformation, what is the new equation?Stretch parallel to the x-axis, scale factor 1/5

Answer 10

y=f(5x)

Question 11

If y=f(x) undergoes the this transformation, what is the new equation?Stretch parallel to the y-axis, scale factor 3

Answer 11

y=f(1/3x)

Question 12

If y=f(x) undergoes the this transformation, what is the new equation?Reflection in the x-axis

Answer 12

y= - f(x)

Question 13

If y=f(x) undergoes the this transformation, what is the new equation?Reflection in the y-axis

Answer 13

y= f(-x)

Question 14

What has happened to the function y=f(x) to make it y=f(x)-6?

Answer 14

Translation, 6 units down in the y-direction

Question 15

What has happened to the function y=f(x) to make it y=f(x)+12?

Answer 15

Translation, 12 units up in the y-direction