Chapter 6.4, Problem 22Q

To determine

To write: The rule for the function $g$ if $f\left(x\right)=3^x$ .

Answer to Problem 22Q

The rule for the function $g$ is $g\left(x\right)=3^x-4$ .

Explanation of Solution

Given information:

The graph of $g$ is a transformation of the graph of $f$ and the function is $f\left(x\right)=3^x$ .

  

Calculation:

The graph of the function $f\left(x\right)=3^x$ is drawn below.

  

From the graph of the function $f\left(x\right)=3^x$ and the given graph of function $g\left(x\right)$ , it is clear that the graph is shifted 4 units downwards.

Let the horizontal translation of the function $f\left(x\right)$ is $g\left(x\right)$ .

  $g\left(x\right)=f\left(x\right)-4$

Substitute the value of $f\left(x\right)$ in the above function.

  $g\left(x\right)=-3^x-4$

Therefore, the rule for the function $g$ is $g\left(x\right)=3^x-4$ .