Graph transformations

Question 1

What does f(x) + a do to the graph?
e.g. y = sinx + 2

Answer 1

f(x) moves up by a units
e.g. y = sinx moves up by 2

Question 2

What does f(x) - a do to the graph?
e.g. y = sinx - 2

Answer 2

f(x) moves down by a units
e.g. y = sinx moves down by 2

Question 3

What does f(x - a) do to the graph?
e.g. y = sin(x - 2)

Answer 3

f(x) moves a units to the right
e.g. y = sinx moves 2 units to the right

Question 4

What does f(x + a) do to the graph?
e.g. y = sin(x + 2)

Answer 4

f(x) moves a units to the left
e.g. y = sinx moves 2 units to the left

Question 5

What does -f(x) do to the graph?

Answer 5

f(x) is reflected through the x axis

Question 6

What does f(-x) do to the graph?

Answer 6

f(x) is reflected through the y axis

Question 7

What does af(x) do to the graph?
e.g. y = 2sinx

Answer 7

f(x) stretches vertically by a scale factor of a
e.g. y = sinx is stretched vertically by a scale factor of 2

Question 8

What does f(ax) do to the graph?
e.g. y = sin2x

Answer 8

squashes it horizontally by a scale factor of a
e.g. y = sin x is squashed horizontally be a scale factor of 2