Transformations of a function
The question
(x + 2)³
f(x) = x³, g(x) = (x + 2)³. What happens to the graph?
What happens to the graph?
g(x) = (x + 2)³—inside
bracket = 0atx = −2
Left2
- The change is inside the function — it happens to x first. That changes the input, so the graph moves sideways.
- To get f's starting value, the bracket has to come out 0, and x + 2 is 0 when x = −2. So g does at x = −2 what f did at x = 0 — 2 steps earlier.
- Later along the x-axis is to the right and earlier is to the left, so the graph moves left by 2. Notice the sign in the bracket is the opposite of the direction.
How it works.
- 01
The change is inside the function — it happens to x first. That changes the input, so the graph moves sideways.
- 02
To get f's starting value, the bracket has to come out 0, and x + 2 is 0 when x = −2. So g does at x = −2 what f did at x = 0 — 2 steps earlier.
- 03
Later along the x-axis is to the right and earlier is to the left, so the graph moves left by 2. Notice the sign in the bracket is the opposite of the direction.