Chapter 1.7, Problem 45PPS

(a)

To determine

To graph:The function $f\left(z\right)=-\frac{5}{8}z+87$ and interpret it.

Explanation of Solution

Given:

The given function is,

  $f\left(z\right)=-\frac{5}{8}z+87$

The graph of function $f\left(z\right)=-\frac{5}{8}z+87$ is shown in figure below.

  

Figure (1)

(b)

To determine

To find:The class size that correspond to the average of $72$

Explanation of Solution

Let $f\left(z\right)=72$

So,

  $\begin{array}{c}72=-\frac{5}{8}z+87\\ \frac{5}{8}z=87-72\\ z=\frac{8\left(15\right)}{5}\\ =24\end{array}$

Therefore, the class size is $72$ .

(c)

To determine

To find:The domain and range of the function.

Explanation of Solution

The function is,

  $f\left(z\right)=-\frac{5}{8}z+87$

The domain is the set of real numbers.

The range is also the set of real numbers.