Question

4 select the correct answer. consider the function f(x)=10^x and function g. g(x)=f(x + 4) how will the graph of function g differ from the graph of function f? a. the graph of function g is the graph of function f shifted 4 units to the left. b. the graph of function g is the graph of function f shifted 4 units to the right. c. the graph of function g is the graph of function f shifted 4 units down. d. the graph of function g is the graph of function f shifted 4 units up.

Explanation:

Step1: Recall function - shift rule

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

Step2: Analyze given functions

We have $f(x)=10^{x}$ and $g(x)=f(x + 4)$. Here, $h = 4$. According to the rule, the graph of $g(x)$ is the graph of $f(x)$ shifted 4 units to the left.

Answer:

A. The graph of function $g$ is the graph of function $f$ shifted 4 units to the left.