To answer this question, we start by evaluating the function [tex]\( g(x) = -3x + 4 \)[/tex] at two different points: [tex]\( x = -2 \)[/tex] and [tex]\( x = 4 \)[/tex].
1. Let's calculate [tex]\( g(-2) \)[/tex]:
[tex]\[
g(-2) = -3(-2) + 4
\][/tex]
Simplify the expression:
[tex]\[
g(-2) = 6 + 4 = 10
\][/tex]
Hence, [tex]\( g(-2) = 10 \)[/tex].
2. Next, let's calculate [tex]\( g(4) \)[/tex]:
[tex]\[
g(4) = -3(4) + 4
\][/tex]
Simplify the expression:
[tex]\[
g(4) = -12 + 4 = -8
\][/tex]
Hence, [tex]\( g(4) = -8 \)[/tex].
We now have the values:
[tex]\[
g(-2) = 10 \quad \text{and} \quad g(4) = -8
\][/tex]
3. To compare these values:
- [tex]\( g(-2) = 10 \)[/tex]
- [tex]\( g(4) = -8 \)[/tex]
Clearly, [tex]\( 10 \)[/tex] is larger than [tex]\( -8 \)[/tex].
Therefore, the correct statement is:
- The value of [tex]\( g(-2) \)[/tex] is larger than the value of [tex]\( g(4) \)[/tex].
