The chart below lists the original and sale prices of items at a clothing store.

\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{ Clothing Prices } \\
\hline Original price & Sale price \\
\hline \[tex]$7.99 & \$[/tex]5.59 \\
\hline \[tex]$10.99 & \$[/tex]7.69 \\
\hline \[tex]$12.99 & \$[/tex]9.09 \\
\hline \[tex]$15.99 & \$[/tex]11.19 \\
\hline \[tex]$24.99 & \$[/tex]17.49 \\
\hline \[tex]$29.99 & \$[/tex]20.99 \\
\hline
\end{tabular}

Which statement best describes why the sale price is a function of the original price?

A. As the original price increases, the sale price also increases.
B. The sale price is always less than the original price.
C. For every original price, there is exactly one sale price.
D. The sales price is never less than zero.

Question

08-08-2024
Mathematics

Answered

The chart below lists the original and sale prices of items at a clothing store.

\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{ Clothing Prices } \\
\hline Original price & Sale price \\
\hline \[tex]$7.99 & \$[/tex]5.59 \\
\hline \[tex]$10.99 & \$[/tex]7.69 \\
\hline \[tex]$12.99 & \$[/tex]9.09 \\
\hline \[tex]$15.99 & \$[/tex]11.19 \\
\hline \[tex]$24.99 & \$[/tex]17.49 \\
\hline \[tex]$29.99 & \$[/tex]20.99 \\
\hline
\end{tabular}

Which statement best describes why the sale price is a function of the original price?

A. As the original price increases, the sale price also increases.
B. The sale price is always less than the original price.
C. For every original price, there is exactly one sale price.
D. The sales price is never less than zero.

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-08-08T11:34:48-04:00

To determine why the sale price is a function of the original price, let's analyze the given data and check each of the provided statements in detail.

1. As the original price increases, the sale price also increases:
- We observe the original prices: \[tex]$7.99, \$[/tex]10.99, \[tex]$12.99, \$[/tex]15.99, \[tex]$24.99, \$[/tex]29.99.
- We see that these prices are in increasing order.
- We then look at the corresponding sale prices: \[tex]$5.59, \$[/tex]7.69, \[tex]$9.09, \$[/tex]11.19, \[tex]$17.49, \$[/tex]20.99.
- These prices are also in increasing order.
- Thus, it is true that as the original price increases, the sale price also increases.

2. The sale price is always less than the original price:
- We compare each pair of original and sale prices:
- \[tex]$7.99 > \$[/tex]5.59
- \[tex]$10.99 > \$[/tex]7.69
- \[tex]$12.99 > \$[/tex]9.09
- \[tex]$15.99 > \$[/tex]11.19
- \[tex]$24.99 > \$[/tex]17.49
- \[tex]$29.99 > \$[/tex]20.99
- In every case, the sale price is less than the original price.

3. For every original price, there is exactly one sale price:
- We list the original prices: \[tex]$7.99, \$[/tex]10.99, \[tex]$12.99, \$[/tex]15.99, \[tex]$24.99, \$[/tex]29.99.
- We list the corresponding sale prices: \[tex]$5.59, \$[/tex]7.69, \[tex]$9.09, \$[/tex]11.19, \[tex]$17.49, \$[/tex]20.99.
- Each original price pairs uniquely with one sale price without any repetitions or omissions.
- Therefore, this statement is true.

4. The sale price is never less than zero:
- The lowest sale price listed is \$5.59.
- All the sale prices are positive and none of them are negative or zero.
- Thus, the sale price is never less than zero.

Given these analyses:
- Statement 1: True
- Statement 2: True
- Statement 3: True
- Statement 4: True

All statements are true and valid in describing why the sale price is a function of the original price. However, the reason that best describes the relationship is:

"For every original price, there is exactly one sale price."

This is the defining property of a function, where each input (original price) is associated with exactly one output (sale price).