If f(x) = x³ and g(x) = (x + 1)³, which is the graph of g(x)?

Solution:

Given, the function f(x) = x³

g(x) = (x + 1)³

We have to find the graph of g(x).

By rules of Horizontal transformation,

If y = f(x), then y = f(x + k) gives a function that is translated k units towards the left side.

From the given functions, it is clear that g(x) is a horizontal transformation of f(x) by 1 unit to the left.

i.e. f(x) = f(x + 1)

So, x³ = (x + 1)³

Therefore, the graph of g(x) is a horizontal transformation of f(x).

If f(x) = x³ and g(x) = (x + 1)³, which is the graph of g(x)?

Summary:

If f(x) = x³ and g(x) = (x + 1)³, then the graph of g(x) is a horizontal transformation of f(x) by 1 unit to the left.