Graph Transformations

Question 1

y = f(x)+a

Answer 1

Moves graph a units up

Question 2

y = f(x)-a

Answer 2

Moves graph a units down

Question 3

y = f(x+a)

Answer 3

Moves graph a units to the left

Question 4

y = f(x-a)

Answer 4

Moves graph a units to the right

Question 5

y = -f(x)

Answer 5

Reflection in x axis

Makes all positive y coordinates negative and vice versa

Question 6

y = f(-x)

Answer 6

Reflection in y axis

Makes all positive x coordinates negative and vice versa

Question 7

y = af(x)

Answer 7

Stretch parallel to the y axis with a scale factor of a
Makes graph taller and skinnier
All y-values are multiplied by a with x-values unchanged

Question 8

y = f(ax)

Answer 8

Stretch parallel to x axis with scale factor 1/a
Squashes graph in if a is bigger than 1, Stretches graph out if a is between 0 and 1
All x-values are divided by a, with y-values unchanged