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Evaluate the step function for the given input values.

[tex]\[ g(x) = \left\{
\begin{array}{ll}
-4, & -3 \leq x \ \textless \ -1 \\
-1, & -1 \leq x \ \textless \ 2 \\
3, & 2 \leq x \ \textless \ 4 \\
5, & x \geq 4 \\
\end{array}
\right. \][/tex]

[tex]\[ g(2) = \square \][/tex]

[tex]\[ g(-2) = \square \][/tex]

[tex]\[ g(5) = \square \][/tex]

Sagot :

GinnyAnswer
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]
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