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].
