Question:

At a grocery store, bulk almonds sell for [tex]\$3.80[/tex] per pound. The cost, [tex]y[/tex], in dollars, of [tex]x[/tex] pounds of almonds is shown in the table below:

\begin{tabular}{|c|c|}
\hline
(pounds) & Cost (\$) \\
\hline
0.5 & 1.90 \\
\hline
1 & 3.80 \\
\hline
1.5 & 5.70 \\
\hline
2 & 7.60 \\
\hline
\end{tabular}

Choose the correct answer from each drop-down menu:

1. The relation described in the table is [tex]\square[/tex].
2. The domain of the relation is [tex]\square[/tex].
3. The range of the relation is [tex]\square[/tex].



Answer :

Let's tackle the problem step-by-step.

### 1. Identify the relation described by the table:
First, let's observe the given table of values:

[tex]\[ \begin{tabular}{|c|c|} \hline (pounds) & $y$ (dollars) \\ \hline 0.5 & 1.90 \\ \hline 1 & 3.80 \\ \hline 1.5 & 5.70 \\ \hline 2 & 7.60 \\ \hline \end{tabular} \][/tex]

From the table, it appears that the cost [tex]\( y \)[/tex] is directly proportional to the weight [tex]\( x \)[/tex] of the almonds. This direct proportionality defines a linear relationship between the two variables. Therefore, the relation described in the table is linear.

### 2. Determine the domain of the relation:
The domain of a function is the complete set of all possible values of the independent variable, which in this case, is the weight [tex]\( x \)[/tex] in pounds. From the table, the values of [tex]\( x \)[/tex] are:
[tex]\[ 0.5, 1, 1.5, 2 \][/tex]

Thus, the domain of the relation is [tex]\([0.5, 1, 1.5, 2]\)[/tex].

### 3. Determine the range of the relation:
The range of a function is the complete set of all possible resulting values of the dependent variable, which in this case, is the cost [tex]\( y \)[/tex] in dollars. From the table, the values of [tex]\( y \)[/tex] are:
[tex]\[ 1.90, 3.80, 5.70, 7.60 \][/tex]

Thus, the range of the relation is [tex]\([1.90, 3.80, 5.70, 7.60]\)[/tex].

### Final answers for the drop-down menu:
So, the correct answers for the drop-down menu would be as follows:

1. The relation described in the table is linear.
2. The domain of the relation is [tex]\([0.5, 1, 1.5, 2]\)[/tex].
3. The range of the relation is [tex]\([1.90, 3.80, 5.70, 7.60]\)[/tex].