Chapter 8.3, Problem 6CYU

a.

To determine

To write an equation representing the cost of each friend as a function of how many friends give.

Answer to Problem 6CYU

The required function is $c=\frac{150}{f}$ .

Explanation of Solution

Given information:

The given statement is:

“A group of friends plans to get their youth group leader a gift certificate for a day at a spa. The certificate costs $\$150$ .”

The cost of each friend is $\text{c}$ and the number of friends is $\text{f}$ .

The equation representing the cost of each friend as a function of how many friends give can be written as:

  $c=\frac{150}{f}$ .

Hence, the required function is $c=\frac{150}{f}$ .

b.

To determine

To graph the function and state the domain and range.

Explanation of Solution

Given information:

The given function is:

  $c=\frac{150}{f}$

Graph:

This represents a transformation of the graph of $f\left(x\right)=\frac{1}{x}$ .

  $a=150$ : The graph is expanded.

  $h=0$ : There is an asymptote at $f=0$ .

  $k=0$ : There is an asymptote at $c=0$ .

The graph of the function is:

  

Interpretation:

The domain of the graph is all real numbers not equal to $0$ and the range is all real numbers except $0$ .

c.

To determine

To explain any limitations to the range or domain in this situation.

Answer to Problem 6CYU

In this situation, the domain and range are limited to all the positive numbers (greater than zero) because the negative numbers will not make sense.

Explanation of Solution

Given information:

The given statement is:

“A group of friends plans to get their youth group leader a gift certificate for a day at a spa. The certificate costs $\$150$ .”

The function is $c=\frac{150}{f}$ .

In this situation, the domain and range are limited to all the positive numbers (greater than zero) because the negative numbers will not make sense.