Question

evaluate the function. (see example 1)
\\( g(x) = \

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

1. \\( g(-1) \\)

1. \\( g(0) \\)

Explanation:

Problem 8: Evaluate \( g(-1) \)

Step1: Determine the applicable piece

Since \( x = -1 \) and the first piece is defined for \( x \leq -1 \), we use \( g(x) = -x + 4 \).

Step2: Substitute \( x = -1 \)

Substitute \( x = -1 \) into \( -x + 4 \):
\( -(-1) + 4 = 1 + 4 = 5 \)

Step1: Determine the applicable piece

Since \( -1 < 0 < 2 \), we use the second piece \( g(x) = 3 \).

Step2: Get the value

For this piece, the function value is always 3, so \( g(0) = 3 \).

Answer:

\( 5 \)

Problem 9: Evaluate \( g(0) \)