Chapter 7.6, Problem 4CYU

To determine

Find the translation of the given function $f\left(x\right)=3^x$ with respect to the given function graph.

Answer to Problem 4CYU

The graph of $g\left(x\right)=3^{x+2}-4$ is sifted $2-unit$ in negative $x-axis$ and also shifted $4-unit$ in negative $y-axis$ .

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)=3^{x+2}-4$

By adding $"2"$ in exponential part and also subtracted $"5"$ of $f\left(x\right)=3^x$ then $g\left(x\right)=3^{x+2}-4$ is arrived

So, by the concept of translation of graph when something is added in the exponential part and subtracting of the parent function then the graph is shifted in negative $x-axis$ same as the unit added in the exponential and subtracted in non-exponential part of parent function then the graph is shifted in negative $y-axis$ .

So, the graph of $g\left(x\right)=3^{x+2}-4$ is sifted $2-unit$ in negative $x-axis$ and also shifted $4-unit$ in negative $y-axis$ .