Question 2 (5 points)

[tex]\[
h(x)=\left\{
\begin{array}{cc}
-4x + 2 & \text{if } x \leq -5 \\
x + 7 & \text{if } -5 \ \textless \ x \ \textless \ 5 \\
3x - 5 & \text{if } x \geq 5
\end{array}
\right.
\][/tex]

Given the piecewise function shown, find the value of [tex]\( h(-6) \)[/tex].

A. 26
B. -23
C. 1
D. -6



Answer :

To find the value of [tex]\( h(-6) \)[/tex] for the given piecewise function [tex]\( h(x) \)[/tex], let's follow the steps methodically.

The piecewise function is defined as follows:
[tex]\[ h(x) = \begin{cases} -4x + 2 & \text{if } x \leq -5 \\ x + 7 & \text{if } -5 < x < 5 \\ 3x - 5 & \text{if } x \geq 5 \end{cases} \][/tex]

Step 1: Identify the correct interval for [tex]\( x = -6 \)[/tex].

We need to determine which case of the piecewise function applies to [tex]\( x = -6 \)[/tex]:
[tex]\[ x \leq -5 \][/tex]

Since [tex]\( -6 \)[/tex] is less than or equal to [tex]\( -5 \)[/tex], we use the first part of the piecewise function:
[tex]\[ h(x) = -4x + 2 \][/tex]

Step 2: Substitute [tex]\( x = -6 \)[/tex] into the appropriate piece of the function.

[tex]\[ h(-6) = -4(-6) + 2 \][/tex]

Step 3: Perform the arithmetic operations:

[tex]\[ -4(-6) = 24 \][/tex]

[tex]\[ 24 + 2 = 26 \][/tex]

So, the value of [tex]\( h(-6) \)[/tex] is:

[tex]\[ h(-6) = 26 \][/tex]

Thus, the correct answer is [tex]\(\boxed{26}\)[/tex].