the graphs of f(x)=5^x and its translation, g(x), are shown on the graph. what is the equation of g(x)…

Explanation:

Step1: Recall translation rules

The general form of a vertical translation of a function $y = f(x)$ is $y=f(x)+k$, where $k$ is the amount of vertical shift. If $k>0$, the graph shifts up; if $k < 0$, the graph shifts down.

Step2: Identify the shift

The point $(0,1)$ on $f(x)=5^{x}$ is translated to the point $(0, - 9)$ on $g(x)$. The change in the $y -$coordinate is $-9 - 1=-10$. This means the graph of $f(x)$ is shifted down by 10 units.

Step3: Write the equation of $g(x)$

Since $f(x)=5^{x}$ and it is shifted down 10 units, the equation of $g(x)$ is $g(x)=5^{x}-10$.

Answer:

$g(x)=5^{x}-10$