If f(x) = x³, which of the following describes the graph of f(x + 2)?
The graph of f(x + 2) is a horizontal shift of f(x) = x³ two units to the left.
The graph of f(x + 2) is a horizontal shift of f(x) = x³ two units to the right.
The graph of f(x + 2) is a vertical shift of f(x) = x³ two units up.
The graph of f(x + 2) is a vertical shift of f(x) = x³ two units down. 

Solution:

Given, function f(x) = x³

We have to find the graph that describes the graph of f(x + 2).

Let us understand the transformation of f(x) to f(x+3) and the transformation of f(x) to f(x+2).

The above graph describes the graph of f(x - 3) if f(x) = x³.

The red line indicates graph of f(x)

The blue line indicates graph of f(x - 3)

It is clear that the graph of f(x - 3) is shifted horizontally to three units to the right from the graph of f(x).

The red line indicates graph of f(x)

The blue line indicates graph of f(x + 2)

So, the graph of f(x + 2) is shifted horizontally to two units to the left from the graph of f(x).

Therefore, the graph of f(x + 2) is a horizontal shift of f(x) = x³ two units to the left.

If f(x) = x³, which of the following describes the graph of f(x + 2)?

Summary:

If f(x) = x³, the graph of f(x + 2) is a horizontal shift of f(x) = x³ two units to the left.