Question

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

Answer 1

C

Explanation:

In translating graphs of functions, we can follow 2 rules:

1. The graph of
`f(x)+a` is the graph of
`f(x)` shifted a units UP VERTICALLY and the graph of
`f(x)-a` is the graph of
`f(x)` shifted a units DOWN VERTICALLY.

2. The graph of
`f(x+a)` is the graph of
`f(x)` shifted a units to the LEFT HORIZONTALLY and the graph of
`f(x-a)` is the graph of
`f(x)` shifted a units RIGHT HORIZONTALLY.

If we understand the 2 rules above, we clearly know that f(x+2) will be a horizontal shift to the LEFT, of course, with respect to the function
`f(x)=x^3`. Looking at the answer choices, C is right.