Graph Transformations

Question 1

What is the general rule for graph transformations?

Answer 1

Outside - y-coordinate - as expected
Inside - x-coordinate - opposite

Question 2

What will happen to: y = -f(x)?

Answer 2

It’s outside, so affects the y-coordinate, but since it is a negative, the graph is reflected oppositely, so into the x-axis, because the y-coordinates are negated.

Question 3

What will happen to: y = f(-x)?

Answer 3

It’s inside, so affects the x-coordinate oppositely, so the graph is reflected into the y-axis, because the x-coordinates are negated.

Question 4

What will happen to y = af(x)?

Answer 4

It’s outside, so affects the y-coordinate as expected, so the graph streches, because the y-coordinates are being multiplied by ‘a’.

Question 5

What will happen to y = f(ax)?

Answer 5

It’s inside, so affects the x-coordinate oppositely, so the graph is compressed, because the x-coordinates are multiplied by ‘a’.