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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.

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Answer:

C

Step-by-step explanation:

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

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

2. The graph of  [tex]f(x+a)[/tex]  is the graph of   [tex]f(x)[/tex]  shifted a units to the LEFT HORIZONTALLY and the graph of  [tex]f(x-a)[/tex]  is the graph of  [tex]f(x)[/tex]  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  [tex]f(x)=x^3[/tex]. Looking at the answer choices, C is right.

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