Question

select the correct answer.

consider the function $f(x) = 2^x$ and the function $g(x)$.
$g(x) = f(x + 4) = 2^{(x + 4)}$
how will the graph of $g(x)$ differ from the graph of $f(x)$?

a. the graph of $g(x)$ is the graph of $f(x)$ shifted 4 units to the left.

b. the graph of $g(x)$ is the graph of $f(x)$ shifted 4 units downward.

c. the graph of $g(x)$ is the graph of $f(x)$ shifted 4 units upward.

d. the graph of $g(x)$ is the graph of $f(x)$ shifted 4 units to the right.

Explanation:

To determine how the graph of \( g(x) \) differs from \( f(x) \), we use the rules of function transformations. For a function \( y = f(x + h) \), if \( h>0 \), the graph of \( f(x) \) is shifted \( h \) units to the left. Here, \( g(x)=f(x + 4) \) with \( h = 4>0 \), so the graph of \( g(x) \) is the graph of \( f(x) \) shifted 4 units to the left. Option B and C are about vertical shifts (up/down), which would be of the form \( f(x)\pm k \), not applicable here. Option D is a right shift, which would be \( f(x - h) \), not \( f(x + h) \).

Answer:

A. The graph of \( g(x) \) is the graph of \( f(x) \) shifted 4 units to the left.