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 + 8)} )?
a. right
b. up
c. left
d. down

Explanation:

Step1: Recall horizontal shift rule

For a function \( y = f(x) \), the transformation \( y = f(x + h) \) (where \( h>0 \)) shifts the graph of \( f(x) \) to the left by \( h \) units, and \( y = f(x - h) \) shifts it to the right by \( h \) units.

Step2: Analyze the given functions

We have \( f(x)=2^{x} \) and \( g(x) = 2^{(x + 8)} \). Comparing with the horizontal shift formula, here \( h = 8>0 \) and the form is \( f(x+8) \) (since \( g(x)=f(x + 8) \) with \( f(x)=2^{x} \)).

Answer:

C. left