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Consider function [tex]\( g \)[/tex]:

[tex]\[ g(x)=\left\{
\begin{array}{ll}
6, & -8 \leq x \ \textless \ -2 \\
0, & -2 \leq x \ \textless \ 4 \\
-4, & 4 \leq x \ \textless \ 10
\end{array}
\right. \][/tex]

What are the values of the function when [tex]\( x=-2 \)[/tex] and [tex]\( x=4 \)[/tex]?

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

[tex]\[ g(4)= \ \ \ \ \square \][/tex]



Answer :

GinnyAnswer
Let's analyze the piecewise function [tex]\( g(x) \)[/tex] for the given values of [tex]\( x \)[/tex].

The function is defined as:
[tex]\[ g(x) = \begin{cases} 6 & \text{if } -8 \leq x < -2 \\ 0 & \text{if } -2 \leq x < 4 \\ -4 & \text{if } 4 \leq x < 10 \end{cases} \][/tex]

### Step-by-Step Solution:

1. Finding [tex]\( g(-2) \)[/tex]:
- [tex]\( -2 \)[/tex] falls into the interval [tex]\( -2 \leq x < 4 \)[/tex].
- According to the piecewise function definition, [tex]\( g(x) = 0 \)[/tex] for [tex]\( -2 \leq x < 4 \)[/tex].

Therefore, [tex]\( g(-2) = 0 \)[/tex].

2. Finding [tex]\( g(4) \)[/tex]:
- [tex]\( 4 \)[/tex] falls into the interval [tex]\( 4 \leq x < 10 \)[/tex].
- According to the piecewise function definition, [tex]\( g(x) = -4 \)[/tex] for [tex]\( 4 \leq x < 10 \)[/tex].

Therefore, [tex]\( g(4) = -4 \)[/tex].

### Final Values:
[tex]\[ g(-2) = 0 \][/tex]
[tex]\[ g(4) = -4 \][/tex]

So, the values of the function at [tex]\( x = -2 \)[/tex] and [tex]\( x = 4 \)[/tex] are:
[tex]\[ g(-2) = 0 \][/tex]
[tex]\[ g(4) = -4 \][/tex]

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