To determine the domain and range of the function represented by the given table, we need to analyze the provided [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values.
The table of values is:
[tex]\[
\begin{tabular}{|l|c|c|c|c|c|}
\hline
$x$ & -1 & -0.5 & 0 & 0.5 & 1 \\
\hline
$y$ & 3 & 4 & 5 & 6 & 7 \\
\hline
\end{tabular}
\][/tex]
### Step-by-Step Solution:
1. Domain:
The domain of a function consists of all the unique [tex]\(x\)[/tex] values for which the function is defined. From the table, we see that the [tex]\(x\)[/tex] values are:
[tex]\[
x = \{-1, -0.5, 0, 0.5, 1\}
\][/tex]
2. Range:
The range of a function consists of all the unique [tex]\(y\)[/tex] values that the function takes. From the table, we see that the [tex]\(y\)[/tex] values are:
[tex]\[
y = \{3, 4, 5, 6, 7\}
\][/tex]
Given these observations, we compare the possible answers:
- Option A:
- Domain: [tex]\(\{-1, -0.5, 0, 0.5, 1\}\)[/tex]
- Range: [tex]\(\{3, 4, 5, 6, 7\}\)[/tex]
- Option B:
- Domain: [tex]\(\{-1, -0.5, 0, 0.5, 1\}\)[/tex]
- Range: [tex]\(y \geq 3\)[/tex]
- Option C:
- Domain: [tex]\(-1 \leq x \leq 1\)[/tex]
- Range: [tex]\(\{3, 4, 5, 6, 7\}\)[/tex]
- Option D:
- Domain: [tex]\(-1 \leq x \leq 1\)[/tex]
- Range: [tex]\(y \geq 3\)[/tex]
### Analysis of Options:
- Option A correctly lists the individual [tex]\(x\)[/tex] values and [tex]\(y\)[/tex] values.
- Option B correctly lists the individual [tex]\(x\)[/tex] values but incorrectly describes the range as [tex]\(y \geq 3\)[/tex], which implies all [tex]\(y\)[/tex] values greater than or equal to 3 without specifying the specific values.
- Option C correctly describes the domain as [tex]\( -1 \leq x \leq 1 \)[/tex] but should have listed each individual [tex]\(x\)[/tex] value.
- Option D incorrectly describes both the domain and range as ranges of values rather than the specific values given in the table.
Thus, the correct answer is:
A. Domain: [tex]\(\{-1, -0.5, 0, 0.5, 1\}\)[/tex] Range: [tex]\(\{3, 4, 5, 6, 7\}\)[/tex]
