Answered

[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-5 & 9 \\
\hline
1 & 0 \\
\hline
4 & -7 \\
\hline
6 & -1 \\
\hline
\end{array}
\][/tex]

What is the range of the given function?

A. [tex]\(\{x \mid x=-5,1,4,6\}\)[/tex]

B. [tex]\(\{y \mid y=-7,-1,0,9\}\)[/tex]

C. [tex]\(\{x \mid x=-7,-5,-1,0,1,4,6,9\}\)[/tex]

D. [tex]\(\{y \mid y=-7,-5,-1,0,1,4,6,9\}\)[/tex]



Answer :

GinnyAnswer
To determine the range of the given function, we need to focus on the possible [tex]\( y \)[/tex] values listed in the table. Let's go through this step-by-step:

1. Identify the given [tex]\( y \)[/tex] values from the table:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -5 & 9 \\ \hline 1 & 0 \\ \hline 4 & -7 \\ \hline 6 & -1 \\ \hline \end{array} \][/tex]

2. Extract the [tex]\( y \)[/tex] values:
- For [tex]\( x = -5 \)[/tex], [tex]\( y = 9 \)[/tex]
- For [tex]\( x = 1 \)[/tex], [tex]\( y = 0 \)[/tex]
- For [tex]\( x = 4 \)[/tex], [tex]\( y = -7 \)[/tex]
- For [tex]\( x = 6 \)[/tex], [tex]\( y = -1 \)[/tex]

3. List all the [tex]\( y \)[/tex] values:
[tex]\[ y = 9, 0, -7, -1 \][/tex]

4. Sort the [tex]\( y \)[/tex] values in ascending order:
[tex]\[ y = -7, -1, 0, 9 \][/tex]

5. Define the range:
The range of the function is the set of all [tex]\( y \)[/tex] values that the function can output.

Therefore, the range of the given function is [tex]\(\{y \mid y = -7, -1, 0, 9\}\)[/tex].

Hence, the correct answer is:
[tex]\[ \{y \mid y = -7, -1, 0, 9\} \][/tex]

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