Chapter 7.6, Problem 55PPS

To determine

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

Answer to Problem 55PPS

  $j(x)=-2f(x+2)$

Explanation of Solution

Given:

  

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

Calculation:

Let,

  $\begin{array}{l}\Rightarrow y=-af(x+b)\\ \Rightarrow y=-a{\left(\frac{3}{2}\right)}^{x+b}\mathrm{....................}(i)\end{array}$

Where a and b are constants.

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

The above format matches only one function, which is:

  $j(x)=-2f(x+2)\Rightarrow j(x)=-2{\left(\frac{3}{2}\right)}^{x+2}$

Verification:

Using graphing utility tool, the graph is plotted and compared with the given graph.

(i(ii)

Interpretation:

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

Conclusion:

Hence, the function for the given graph is $j(x)=-2f(x+2)$ .