Chapter 4.6, Problem 5P

(a)

To determine

The reasonable domain and range for problem $5$ is to be calculated.

Explanation of Solution

A relation is represented as a set of ordered pairs $\left(x,y\right)$ .

The set of $x$ values is known as domain and the set of values of $y$ is known as range.

The data of problem $5$ is given below:

The function is,

  $A\left(q\right)=100q$

Where,

• A represents the area in square foot.
• q represents the quarts of paint cover.

Area covered by a quart of paint = $100{\text{ft}}^{\text{2}}$

Given amount of paint = $\text{7}\text{qt}$

The least amount of paint that can be used is none. Therefore the least domain value is $\text{0}$ .

The most amount of paint can be used is the given amount of paint which is $\text{7}\text{qt}$ . Therefeore the greatest domain value is $\text{3}$ .

The domain is represented as follows:

  $0\le \text{qt}\le 7$

The range is calculated as follows:

Plugin the least value and greatest value of domain in the function to calculate the range

  $\begin{array}{l}A\left(0\right)=100\times 0\\ =0\\ A\left(7\right)=100\times 7\\ =700{\text{ft}}^{\text{2}}\end{array}$

The range is,

  $0\le A\left(q\right)\le 700$

(b)

To determine

The domain values of problem $5$ are to be analyzed.

Explanation of Solution

The function in the problem $5$ is,

The function is,

  $A\left(q\right)=100q$

Where,

• A represents the area in square foot.
• q represents the quarts of paint cover.

Area covered by a quart of paint = $100{\text{ft}}^{\text{2}}$

Given amount of paint = $3\text{qt}$

The least domain value is $\text{0}$ .

The greatest domain value is $3$ .

The relation forms order pairs.

The domain values are defined on the basis of set of $x$ values.

The given relation represents the area cover by the amount of paint. The area covered by the paint is calculated using the domain.

There are possibilities either use the full amount of given paint or none. The area covered for value of $q$ less than zero, does not make any sense as the area covered cannot be negative.

The value of domain cannot be greater than $3$ since the given amount of paint is $3\text{qt}$ .