Question

the graph of function $g$ is a translation of the graph of parent function $f(x)=2^x$.
the graph of $f$ is translated is added, so $g(x)=2^x + k$. how of each function to find the valu
try again
write an equation for function $g$.
use the number pad and $x$ to enter your answer in the box.
$g(x) = \square$

Explanation:

Step1: Identify parent function point

For $f(x)=2^x$, when $x=0$, $f(0)=2^0=1$. So $f(x)$ passes through $(0,1)$.

Step2: Find corresponding g(x) point

From the graph, $g(x)$ passes through $(0,-4)$ at the same x-value.

Step3: Calculate vertical shift

Let $g(x)=2^x + k$. Substitute $(0,-4)$:
$-4 = 2^0 + k$
$-4 = 1 + k$
$k = -4 - 1 = -5$

Step4: Form g(x) equation

Substitute $k=-5$ into the translation form.

Answer:

$g(x)=2^x - 5$