The graph f(x)=3^x is reflected across the cacos shifted downward 5 units and the. Shifted left 2 units. Let g(x) represent the new function. What is an equation for this function? G(x) =? What is the y-intercept of g(x) enter as ordered pair. What is the domain of g(x)? Enter as interval. What is the range of g(x) enter as interval.

Given:

The graph of $f\left(x\right)=3^x$ is reflected across the x axis, shifted downward 5 units and then shifted left 2 units.

Reflection across x axis:

To reflect the graph of the function $y=f\left(x\right)$ about the x axis, multiply $f\left(x\right)$ by $-1$.

Thus, the graph of the function $y=-f\left(x\right)$ is the reflection of the graph of $y=f\left(x\right)$ about the x axis.

Vertical shift:

The graph of $y=f\left(x\right)-h$ is the graph of $y=f\left(x\right)$ shifted down h units where $h>0$.

Horizontal shift:

The graph of $y=f\left(x+h\right)$ is the horizontal shift of graph of $y=f\left(x\right)$ to the left by h units where $h>0$.

By the above definitions, the graph of $y=-3^x$ is the reflection of the graph of $y=3^x$ across the x axis.

The graph of $y=-3^x-5$ is the  graph of $y=-3^x$ shifted down  5 units.

The graph of $y=-3^{x+2}-5$ is the graph of $y=-3^x-5$ shifted to the left by 2 units.

Therefore, the new function is $y=-3^{x+2}-5$.

Let the new function be $g\left(x\right)$.

Therefore, the equation for this function is $g\left(x\right)=\boxed{-3^{x+2}-5}$.