Answer: g(x) = (x - 1)^3
Step-by-step explanation:
There is a transformation called "horizontal translation"
For an initial function f(x), a horizontal translation of N is written as:
g(x) = f(x - N)
where if N is positive, we have a translation of N units to the right.
If N is negative, we have a translation of N units to the left.
Here, we can see that:
f(x) = x^3, such that when x = 0, f(0) = 0.
And g(x) seems to be a horizontal translation of f(x) (because the graph of g(x) is equidistant to the graph of f(x)), then:
g(x) = (x - N)^3
And we can see that when x = 0, g(0) = 1
Then:
g(0) = (0 - N)^3 = 1
N^3 = 1
N = ∛1 = 1
Then the equation for g(x) is:
g(x) = (x - 1)^3
