Answer :
To determine the value of [tex]\( x \)[/tex] when [tex]\( f(x) = -3 \)[/tex], we need to carefully analyze the provided table of values.
Here's the table for reference:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -4 & -66 \\ \hline -3 & -29 \\ \hline -2 & -10 \\ \hline -1 & -3 \\ \hline 0 & -2 \\ \hline 1 & -1 \\ \hline 2 & 6 \\ \hline \end{array} \][/tex]
We are interested in the value of [tex]\( x \)[/tex] where [tex]\( f(x) = -3 \)[/tex].
1. Find [tex]\( -3 \)[/tex] in the [tex]\( f(x) \)[/tex] column of the table.
2. Look at the corresponding value of [tex]\( x \)[/tex] in the same row.
Let's search for [tex]\( -3 \)[/tex] in the [tex]\( f(x) \)[/tex] column:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -4 & -66 \\ \hline -3 & -29 \\ \hline -2 & -10 \\ \hline -1 & \mathbf{-3} \\ \hline 0 & -2 \\ \hline 1 & -1 \\ \hline 2 & 6 \\ \hline \end{array} \][/tex]
We observe that when [tex]\( f(x) = -3 \)[/tex], the corresponding [tex]\( x \)[/tex] value is [tex]\( -1 \)[/tex].
Thus, the solution is:
[tex]\[ x = -1 \text{ when } f(x) = -3 \][/tex]
Therefore, the correct answer is [tex]\( -1 \)[/tex].
Here's the table for reference:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -4 & -66 \\ \hline -3 & -29 \\ \hline -2 & -10 \\ \hline -1 & -3 \\ \hline 0 & -2 \\ \hline 1 & -1 \\ \hline 2 & 6 \\ \hline \end{array} \][/tex]
We are interested in the value of [tex]\( x \)[/tex] where [tex]\( f(x) = -3 \)[/tex].
1. Find [tex]\( -3 \)[/tex] in the [tex]\( f(x) \)[/tex] column of the table.
2. Look at the corresponding value of [tex]\( x \)[/tex] in the same row.
Let's search for [tex]\( -3 \)[/tex] in the [tex]\( f(x) \)[/tex] column:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -4 & -66 \\ \hline -3 & -29 \\ \hline -2 & -10 \\ \hline -1 & \mathbf{-3} \\ \hline 0 & -2 \\ \hline 1 & -1 \\ \hline 2 & 6 \\ \hline \end{array} \][/tex]
We observe that when [tex]\( f(x) = -3 \)[/tex], the corresponding [tex]\( x \)[/tex] value is [tex]\( -1 \)[/tex].
Thus, the solution is:
[tex]\[ x = -1 \text{ when } f(x) = -3 \][/tex]
Therefore, the correct answer is [tex]\( -1 \)[/tex].
