Question

Identify the transformation from the graph of f(x) = x
3
to g(x) = (x − 4)
3

Answer 1

a shift of 4 units right

Explanation:

Given f(x) then f(x + a) represents a horizontal translation of f(x)

• If a > 0 then shift to the left by a units

• If a < 0 then a shift to the right by a units

Thus for g(x) = (x - 4)³

The graph of g(x) is the graph of f(x) shifted 4 units to the right

Answer 2

The only difference between the two is the "-4" in the second function. This is a vertical translation. g(x) will give the same curve, but 4 units lower on the graph.