Chapter 7.6, Problem 27PPS

To determine

Find the translation of the function.

Answer to Problem 27PPS

The graph of $g\left(x\right)=0.5{\left(2\right)}^{x-1}$ shifted $1-unit$ with respect to positive $x-axis$ and the graph shows vertical compress by $factor-\frac{1}{2}.$

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)=0.5{\left(2\right)}^{x-1}$

Since, $g\left(x\right)=0.5{\left(2\right)}^{x-1}$ so let the parent function be $f\left(x\right)={\left(2\right)}^x$

By multiplying $f\left(x\right)$ to $"0.5"$ and adding $"-1"$ in the exponential part then $g\left(x\right)=0.5{\left(2\right)}^{x-1}$ is arrived

So, by the concept of translation of graph when something negative quantity is adding in the exponential part of function then the graph shifted with respect to positive $x-axis$ and when some quantity which is $>0and<1$ is multiply to the function then the graph shows vertical compress.

So, the graph of $g\left(x\right)=0.5{\left(2\right)}^{x-1}$ shifted $1-unit$ with respect to positive $x-axis$ and the graph shows vertical compress by $factor-\frac{1}{2}.$