To solve the problem, we need to evaluate the function [tex]\(g(x) = -3x + 4\)[/tex] at two specific points: [tex]\(x = -2\)[/tex] and [tex]\(x = 4\)[/tex].
### Step-by-Step Solution
1. Evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = -2\)[/tex]:
[tex]\[
g(-2) = -3(-2) + 4
\][/tex]
Perform the multiplication first:
[tex]\[
g(-2) = 6 + 4
\][/tex]
Then, add the results:
[tex]\[
g(-2) = 10
\][/tex]
2. Evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = 4\)[/tex]:
[tex]\[
g(4) = -3(4) + 4
\][/tex]
Perform the multiplication first:
[tex]\[
g(4) = -12 + 4
\][/tex]
Then, add the results:
[tex]\[
g(4) = -8
\][/tex]
3. Compare [tex]\(g(-2)\)[/tex] and [tex]\(g(4)\)[/tex]:
Now we have [tex]\(g(-2) = 10\)[/tex] and [tex]\(g(4) = -8\)[/tex]. We need to compare these two values.
[tex]\[
10 \text{ (which is } g(-2) \text{) is greater than -8 (which is } g(4) \text{)}
\][/tex]
### Conclusion
Based on the calculations:
- The value of [tex]\(g(-2)\)[/tex] is [tex]\(10\)[/tex].
- The value of [tex]\(g(4)\)[/tex] is [tex]\(-8\)[/tex].
Thus, we can conclude:
The value of [tex]\(g(-2)\)[/tex] is larger than the value of [tex]\(g(4)\)[/tex].
So, the correct statement is:
- The value of [tex]\(g(-2)\)[/tex] is larger than the value of [tex]\(g(4)\)[/tex].
