Sure! Let’s evaluate the step function [tex]\( g(x) \)[/tex] for the given input values [tex]\( x = 2 \)[/tex], [tex]\( x = -2 \)[/tex], and [tex]\( x = 5 \)[/tex].
### Step-by-Step Solution
1. Evaluate [tex]\( g(2) \)[/tex]:
- First, identify which interval [tex]\( 2 \)[/tex] falls into:
[tex]\[
2 \leq x < 4
\][/tex]
- According to the function definition, in this interval, the value of [tex]\( g(x) \)[/tex] is [tex]\( 3 \)[/tex].
[tex]\[
g(2) = 3
\][/tex]
2. Evaluate [tex]\( g(-2) \)[/tex]:
- Identify which interval [tex]\( -2 \)[/tex] falls into:
[tex]\[
-3 \leq x < -1
\][/tex]
- According to the function definition, in this interval, the value of [tex]\( g(x) \)[/tex] is [tex]\( -4 \)[/tex].
[tex]\[
g(-2) = -4
\][/tex]
3. Evaluate [tex]\( g(5) \)[/tex]:
- Identify which interval [tex]\( 5 \)[/tex] falls into:
[tex]\[
x \geq 4
\][/tex]
- According to the function definition, in this interval, the value of [tex]\( g(x) \)[/tex] is [tex]\( 5 \)[/tex].
[tex]\[
g(5) = 5
\][/tex]
### Conclusion
Therefore, the values of the step function [tex]\( g(x) \)[/tex] for the input values [tex]\( x = 2 \)[/tex], [tex]\( x = -2 \)[/tex], and [tex]\( x = 5 \)[/tex] are:
[tex]\[
g(2) = 3
\][/tex]
[tex]\[
g(-2) = -4
\][/tex]
[tex]\[
g(5) = 5
\][/tex]
