Question

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

$$\begin{cases} -5|x| + 7 & \\text{for } x \\leq -2 \\\\ 2x + 3 & \\text{for } -2 < x < 5 \\\\ 6 & \\text{for } x \\geq 5 \\end{cases}$$

\\)

part 1 of 5
\\( g(-4) = \square \\)

part 2 of 5
\\( g(5) = \square \\)

part 3 of 5
\\( g(-2) = \square \\)

part 4 of 5
\\( g(0) = \square \\)

part 5 of 5
\\( g(6) = \square \\)

Explanation:

Part 1: \( g(-4) \)

Step1: Determine the function rule

Since \( -4 \leq -2 \), use \( g(x) = -5|x| + 7 \).

Step2: Substitute \( x = -4 \)

\( g(-4) = -5|-4| + 7 \)

Step3: Calculate the absolute value

\( |-4| = 4 \), so \( g(-4) = -5(4) + 7 \)

Step4: Simplify the expression

\( -5(4) = -20 \), then \( -20 + 7 = -13 \)

Step1: Determine the function rule

Since \( 5 \geq 5 \), use \( g(x) = 6 \).

Step2: Substitute \( x = 5 \)

\( g(5) = 6 \)

Step1: Determine the function rule

Since \( -2 \leq -2 \), use \( g(x) = -5|x| + 7 \).

Step2: Substitute \( x = -2 \)

\( g(-2) = -5|-2| + 7 \)

Step3: Calculate the absolute value

\( |-2| = 2 \), so \( g(-2) = -5(2) + 7 \)

Step4: Simplify the expression

\( -5(2) = -10 \), then \( -10 + 7 = -3 \)

Answer:

\( -13 \)

Part 2: \( g(5) \)