Question

select the correct answer.
in which direction must the graph of $f(x) = 2^x$ be shifted to produce the graph of $g(x) = 2^{(x - 7)}$?
a. up
b. left
c. down
d. right

Explanation:

Step1: Recall the rule for horizontal shifts of functions

For a function \( y = f(x) \), the transformation \( y = f(x - h) \) represents a horizontal shift. If \( h>0 \), the graph shifts to the right by \( h \) units; if \( h < 0 \), the graph shifts to the left by \( |h| \) units.

Step2: Compare \( f(x)=2^{x} \) and \( g(x)=2^{(x - 7)} \)

Here, \( g(x)=f(x - 7) \) (since \( f(x)=2^{x} \), so \( f(x - 7)=2^{(x - 7)} \)). Using the horizontal shift rule, \( h = 7>0 \), so the graph of \( f(x) \) is shifted to the right by 7 units to get the graph of \( g(x) \).

Answer:

D. right