Question

evaluate the step function for the given input values.
\\( g(x) = \

$$\begin{cases} -4, & -3 \\leq x < -1 \\\\ -1, & -1 \\leq x < 2 \\\\ 3, & 2 \\leq x < 4 \\\\ 5, & x \\geq 4 \\end{cases}$$

\\( g(2) = \square
\\( g(-2) = \square
\\( g(5) = \square

Explanation:

Step1: Evaluate \( g(2) \)

Check which interval \( x = 2 \) belongs to. The interval \( 2 \leq x < 4 \) includes \( x = 2 \), so \( g(2) = 3 \).

Step2: Evaluate \( g(-2) \)

Check which interval \( x = -2 \) belongs to. The interval \( -3 \leq x < -1 \) includes \( x = -2 \), so \( g(-2) = -4 \).

Step3: Evaluate \( g(5) \)

Check which interval \( x = 5 \) belongs to. The interval \( x \geq 4 \) includes \( x = 5 \), so \( g(5) = 5 \).

Answer:

\( g(2) = 3 \)
\( g(-2) = -4 \)
\( g(5) = 5 \)