Question

the exponential function $g(x)=3^{x - 1}-4$ is a transformation of the function $f(x)=3^{x}$. which statements accurately describe how the graph of $g(x)$ compares to the graph of $f(x)$?
select all that apply
$square$ a. $g(x)$ is translated 4 units to the right.
$square$ b. $g(x)$ is translated 4 units down.
$square$ c. $g(x)$ is translated 4 units up.
$square$ d. the horizontal asymptote shifts 1 unit down.
$square$ e. $g(x)$ is translated 1 unit to the right.
$square$ f. $g(x)$ is translated 1 unit to the left.

Explanation:

Step1: Recall translation rules

For $f(x)=b^x$, $g(x)=b^{x-h}+k$ shifts $h$ right/left, $k$ up/down.

Step2: Match to given function

Given $g(x)=3^{x-1}-6$, here $h=1$, $k=-6$.

Step3: Interpret values

$h=1$ means shift 1 unit right. $k=-6$ means shift 6 units down.

Answer:

B. $g(x)$ is translated 6 units down.
E. $g(x)$ is translated 1 unit to the right.