Get the answers you need from a community of experts on IDNLearn.com. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.

Evaluate the step function for the given input values.

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


Sagot :

To evaluate the step function [tex]\( g(x) \)[/tex] for the given input values, we will determine which interval each input value lies in and use the corresponding output value for each interval.

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

1. Evaluate [tex]\( g(2) \)[/tex]:
- Since [tex]\( 2 \leq x < 4 \)[/tex], we fall under the interval [tex]\( 2 \leq x < 4 \)[/tex].
- According to the function definition, [tex]\( g(x) = 3 \)[/tex] for [tex]\( 2 \leq x < 4 \)[/tex].
- Therefore, [tex]\( g(2) = 3 \)[/tex].

2. Evaluate [tex]\( g(-2) \)[/tex]:
- Since [tex]\( -3 \leq x < -1 \)[/tex], we fall under the interval [tex]\( -3 \leq x < -1 \)[/tex].
- According to the function definition, [tex]\( g(x) = -4 \)[/tex] for [tex]\( -3 \leq x < -1 \)[/tex].
- Therefore, [tex]\( g(-2) = -4 \)[/tex].

3. Evaluate [tex]\( g(5) \)[/tex]:
- Since [tex]\( x \geq 4 \)[/tex], we fall under the interval [tex]\( x \geq 4 \)[/tex].
- According to the function definition, [tex]\( g(x) = 5 \)[/tex] for [tex]\( x \geq 4 \)[/tex].
- Therefore, [tex]\( g(5) = 5 \)[/tex].

So, the evaluated values are:
[tex]\[ g(2) = 3, \quad g(-2) = -4, \quad g(5) = 5 \][/tex]

In conclusion:
[tex]\[ \begin{array}{l} g(2) = 3 \\ g(-2) = -4 \\ g(5) = 5 \end{array} \][/tex]