Chapter 7.6, Problem 57PPS

To determine

To find a match to the given graph with the given list of functions

Answer to Problem 57PPS

  $p(x)=f(5x)$

Explanation of Solution

Given:

  

Also, the parent functions: $f(x)={\left(\frac{3}{2}\right)}^x$

Calculation:

Let,

  $\begin{array}{l}\Rightarrow y=f(ax)\\ \Rightarrow y={\left(\frac{3}{2}\right)}^{ax}\mathrm{....................}(i)\end{array}$

Where a is constant.

Now, equation ( i ) is compared with the list of functions given.

The above format matches only one function, which is:

  $q(x)=\frac{1}{5}f(x)\Rightarrow q(x)=\frac{1}{5}{\left(\frac{3}{2}\right)}^x$

Verification:

  i(ii)

Interpretation:

When both the above graphs are compared it is clear that they are same, which means the calculations done is correct.

Conclusion:

Hence, the function for the given graph is $p(x)=f(5x)$ .