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

Answer:

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

Explanation:

Step1: Identify vertical - shift

The general form of a vertical translation of a function $y = f(x)$ is $y=f(x)+k$, where $k$ is the vertical - shift.

Step2: Analyze the y - intercepts

For $f(x)=5^{x}$, when $x = 0$, $f(0)=5^{0}=1$. For $g(x)$, when $x = 0$, from the graph $g(0)=-9$.

Step3: Calculate the value of k

We know that $g(x)=5^{x}+k$. Substituting $x = 0$, $g(0)=5^{0}+k$. Since $g(0)=-9$ and $5^{0}=1$, we have $1 + k=-9$. Solving for $k$, we get $k=-10$. So $g(x)=5^{x}-10$.