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]
