If f(x) = x^3, which of the following describes the graph of f(x + 2)?

Question

A.The graph of f(x + 2) is a horizontal shift of f(x) = x^3 two units to the left.

B.The graph of f(x + 2) is a horizontal shift of f(x) = x^3 two units to the right.

C.The graph of f(x + 2) is a vertical shift of f(x) = x^3 two units up.

D.The graph of f(x + 2) is a vertical shift of f(x) = x^3 two units down.

Answer 1

Correct answer is A.

 

Visualize this:

The graph of f(x) = x³ crosses the x-axis at x=0.

 

The graph of f(x+2)=(x+2)³ crosses the x-axis at x=-2 (x+2=0, then x=-2). So, each point of f(x) shifts 2 units to the left.

Answer 2

I would go with A.