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Evaluating Functions

Use the table to answer the following questions. Separate multiple answers with commas if needed.

\begin{tabular}{|c|r|r|r|r|r|r|r|r|r|r|}
\hline
[tex]$x$[/tex] & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
[tex]$g(x)$[/tex] & -27 & -62 & 43 & -75 & -30 & 3 & -68 & -33 & -27 & -93 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline
Evaluate [tex]$g(3):$[/tex] & [tex]$g(3)=\square$[/tex] \\
\hline
For what value(s) of [tex]$x$[/tex] does [tex]$g(x)=-27?$[/tex] & [tex]$x=\square$[/tex] \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To solve this problem, we'll use the given table to evaluate two specific questions. Let's walk through each one step-by-step.

### Question 1: Evaluate [tex]\( g(3) \)[/tex]

1. Locate the value of [tex]\( x = 3 \)[/tex] in the top row of the table.
2. Look directly below it in the bottom row to find [tex]\( g(x) \)[/tex] when [tex]\( x = 3 \)[/tex].

From the table, [tex]\( g(3) = -75 \)[/tex].

So, the answer is:
[tex]\[ g(3) = -75 \][/tex]

### Question 2: For what value(s) of [tex]\( x \)[/tex] does [tex]\( g(x) = -27 \)[/tex] ?

1. Identify the values in the bottom row that equal [tex]\(-27\)[/tex].
2. Note the corresponding [tex]\( x \)[/tex] values from the top row directly above these [tex]\(-27\)[/tex] values.

From the table:
- When [tex]\( x = 0 \)[/tex], [tex]\( g(x) = -27 \)[/tex]
- When [tex]\( x = 8 \)[/tex], [tex]\( g(x) = -27 \)[/tex]

Therefore, the values of [tex]\( x \)[/tex] for which [tex]\( g(x) = -27 \)[/tex] are:
[tex]\[ x = 0, 8 \][/tex]

### Summary:

#### Evaluate [tex]\( g(3) \)[/tex]:
[tex]\[ g(3) = -75 \][/tex]

#### For what value(s) of [tex]\( x \)[/tex] does [tex]\( g(x) = -27 \)[/tex]?
[tex]\[ x = 0, 8 \][/tex]

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