Answered

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 when [tex]x=4[/tex]?

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

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



Answer :

GinnyAnswer
Let's determine the values of the function [tex]\( g \)[/tex] at specific points.

1. For [tex]\( x = -2 \)[/tex]:
- We need to check which interval [tex]\(-2\)[/tex] falls into.
- Looking at the intervals, [tex]\(-2\)[/tex] is within [tex]\([-2, 4)\)[/tex].
- In this interval, the function [tex]\( g(x) \)[/tex] is defined as [tex]\( 0 \)[/tex].

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

2. For [tex]\( x = 4 \)[/tex]:
- We need to check which interval [tex]\(4\)[/tex] falls into.
- Looking at the intervals, [tex]\(4\)[/tex] is within [tex]\([4, 10)\)[/tex].
- In this interval, the function [tex]\( g(x) \)[/tex] is defined as [tex]\( -4 \)[/tex].

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

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