Question

find $f(-5)$ for this piecewise-defined function.
$f(x) = \

$$\begin{cases} 5x + 1 & \\text{if } x < -10 \\\\ -3x + 1 & \\text{if } -10 \\leq x \\leq -6 \\\\ 0 & \\text{if } x > -6 \\end{cases}$$

$
write your answer as an integer or as a fraction in simplest form.
$f(-5) = \square$

Explanation:

Step1: Determine the domain for x=-5

We check which part of the piecewise function applies to \( x = -5 \). The conditions are: \( x < -10 \), \( -10 \leq x \leq -6 \), or \( x > -6 \). Since \( -5 > -6 \), we use the third part of the function.

Step2: Evaluate the function at x=-5

The third part of the function is \( f(x) = 0 \) when \( x > -6 \). So, substituting \( x = -5 \) into this part, we get \( f(-5) = 0 \).

Answer:

\( 0 \)