Chapter 7.6, Problem 18PPS

To determine

Find the translation of the given function relates to its parent function.

Answer to Problem 18PPS

The graph of $g\left(x\right)={\left(\frac{2}{5}\right)}^x-1$ is sifted $1-unit$ in negative $y-axis$ .

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)={\left(\frac{2}{5}\right)}^x-1$

Since $g\left(x\right)={\left(\frac{2}{5}\right)}^x-1$ so let the parent function is $p\left(x\right)={\left(\frac{2}{5}\right)}^x$

By subtracting $"1"$ in the non-exponential part of the parent function $p\left(x\right)={\left(\frac{2}{5}\right)}^x$ then $g\left(x\right)={\left(\frac{2}{5}\right)}^x-1$ is arrived

So, by the concept of translation of graph when something is subtracting $"1"$ in the non-exponential part of the parent function then the graph is shifted in negative $y-axis$ .

So, the graph of $g\left(x\right)={\left(\frac{2}{5}\right)}^x-1$ is sifted $1-unit$ in negative $y-axis$ .