Question

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

$$\begin{cases} -5x + 6 & \\text{for } x < -1 \\\\ x^2 + 2 & \\text{for } -1 \\leq x < 5 \\\\ 6 & \\text{for } x \\geq 5 \\end{cases}$$

$
part 1 of 5
$g(2)=\square$
part 2 of 5
$g(-2)=\square$
part 3 of 5
$g(-1)=\square$
part 4 of 5
$g(5)=\square$
part 5 of 5
$g(6)=\square$

Explanation:

Part 1: \( g(2) \)

Step1: Determine the function rule

Since \( -1 \leq 2 \leq 5 \), we use \( g(x) = x^2 + 2 \).

Step2: Substitute \( x = 2 \)

\( g(2) = 2^2 + 2 = 4 + 2 = 6 \).

Step1: Determine the function rule

Since \( -2 < -1 \), we use \( g(x) = -5x + 6 \).

Step2: Substitute \( x = -2 \)

\( g(-2) = -5(-2) + 6 = 10 + 6 = 16 \).

Step1: Determine the function rule

Since \( -1 \) is in the interval \( -1 \leq x \leq 5 \), we use \( g(x) = x^2 + 2 \).

Step2: Substitute \( x = -1 \)

\( g(-1) = (-1)^2 + 2 = 1 + 2 = 3 \).

Answer:

\( 6 \)

Part 2: \( g(-2) \)