Chapter 7.6, Problem 39PPS

To determine

By using the graph of the given function $f\left(x\right)={\left(\frac{1}{2}\right)}^x$ write the value of $n$ for its given equation of $g\left(x\right)$ .

Answer to Problem 39PPS

The value of $n$ is $n=0.5$

So, the equation of $g\left(x\right)=n.f\left(x\right)$ becomes $g\left(x\right)=0.5f\left(x\right)$

Explanation of Solution

Given information:

It is given in the question that, the parent function is $f\left(x\right)={\left(\frac{1}{2}\right)}^x$

And the graph of given function $g\left(x\right)=n.f\left(x\right)$ is,

  

Since the graph of the function $f\left(x\right)={\left(\frac{1}{2}\right)}^x$ is

  

By observing the graph of the two given functions, the graph of $g\left(x\right)=n.f\left(x\right)$ is vertically compress with the $factor-0.5$ which is only possible when the value of $n$ is $n=0.5$

So, the equation of $g\left(x\right)=n.f\left(x\right)$ becomes $g\left(x\right)=0.5f\left(x\right)$