Chapter 7.6, Problem 58PPS

To determine

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

Answer to Problem 58PPS

  $g(x)=-f(x)+2$

Explanation of Solution

Given:

  

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

Calculation:

Let,

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

Where a is constant.

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

The above format matches only one function, which is:

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

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 $g(x)=-f(x)+2$ .