Chapter 2, Problem 1RE

While shopping online for AA batteries, Masoud found that he could order a pack of 8 batteries for $\$6.30,$ a pack of $16$ for $\$13.99,$ a pack of $20$ for $\$12.32,$ or a pack of $24$ for $\$\mathrm{13.99.}$ Define a relation using number of batteries as input and price as output..

What is the domain and range of the relation?

Express the relation as a set of ordered pairs.

Express the relation as a mapping.

Express the relation as a graph.

To determine

The range and domain of a relation, where the relation is defined using number of batteries as input and price as output, with the data Masoud could order a pack of 8 batteries at $\$6.30$, a pack of $16$ for $\$13.99$, a pack of $20$ for $\$12.32$ and a pack of $24$ for $\$13.99$.

Answer to Problem 1RE

Solution:

The domain of the relation is $\{8,16,20,24\}$.

The range of the relation is $\{\$6.30,\$12.32,\$13.99\}$.

Explanation of Solution

Given Information:

Masoud could order a pack of 8 batteries at $\$6.30$, a pack of $16$ for $\$13.99$, a pack of $20$ for $\$12.32$ and a pack of $24$ for $\$13.99$.

Explanation:

The relation is defined as the number of batteries as input and price as output.

The domain is a set of inputs for relation.

Here, the number of batteries is an input for relation.

Therefore, the domain is $\{8,16,20,24\}$.

The range is a set of outputs for relation.

Here, price is an output for relation.

Therefore, the range is $\{\$6.30,\$12.32,\$13.99\}$.

To determine

The relation as a set of order pairs, where the relation is defined using the number of batteries as input and price as output, with the data Masoud could order a pack of 8 batteries at $\$6.30$, a pack of $16$ for $\$13.99$, a pack of $20$ for $\$12.32$ and a pack of $24$ for $\$13.99$.

Answer to Problem 1RE

Solution:

The relation as set of order pairs is $\{(8,6.30),(16,13.99),(20,12.32),(24,13.99)\}$.

Explanation of Solution

Given Information:

Masoud could order a pack of 8 batteries at $\$6.30$, a pack of $16$ for $\$13.99$, a pack of $20$ for $\$12.32$ and a pack of $24$ for $\$13.99$.

Explanation:

A set of order pairs consists of input, number of batteries, as first coordinate and output, price, as second coordinate.

In the relation $R=\left\{\left(x,y\right)|x\in X,y\in Y\right\}$, the domain is the set of all inputs, $x$, and range is the set of all outputs, $y$.

Therefore, the relation as a set of order pairs is $\{(8,6.30),(16,13.99),(20,12.32),(24,13.99)\}$.

To determine

The relation as mapping, where the relation is defined using the number of batteries as input and price as output, with the data Masoud could order a pack of 8 batteries at $\$6.30$, a pack of $16$ for $\$13.99$, a pack of $20$ for $\$12.32$ and a pack of $24$ for $\$13.99$.

Answer to Problem 1RE

Solution:

The mapping is given by

Explanation of Solution

Given Information:

Masoud could order a pack of 8 batteries at $\$6.30$, a pack of $16$ for $\$13.99$, a pack of $20$ for $\$12.32$ and a pack of $24$ for $\$13.99$.

Explanation:

For mapping, consider $n$ for number of batteries and $p$ for price.

Thus, the mapping is:

To determine

To graph: A scatter plot of a relation, where the relation is defined using the number of batteries as input and price as output, with the data Masoud could order a pack of 8 batteries at $\$6.30$, a pack of $16$ for $\$13.99$, a pack of $20$ for $\$12.32$ and a pack of $24$ for $\$13.99$.

Explanation of Solution

Given Information:

Masoud could order a pack of 8 batteries at $\$6.30$, a pack of $16$ for $\$13.99$, a pack of $20$ for $\$12.32$ and a pack of $24$ for $\$13.99$.

Graph:

The scatter plot of given data is:

Interpretation:

The scatter plot represents thenumber of batteries as the independent variable and price in dollars as the dependent variable.