Question

find f(-5) for this piecewise-defined function.

f(x) = \

$$\begin{cases} \\frac{2}{5}x + 3 & \\text{if } x \\leq -10 \\\\ -2x + 5 & \\text{if } -10 < x < -4 \\\\ -5x + 7 & \\text{if } x \\geq -4 \\end{cases}$$

write your answer as an integer or as a fraction in simplest form.

f(-5) = \boxed{}

Explanation:

Step1: Determine the interval for \( x = -5 \)

We check which piece of the piecewise function applies to \( x = -5 \). The intervals are \( x \leq -10 \), \( -10 < x < -4 \), and \( x \geq -4 \). Since \( -10 < -5 < -4 \), we use the second piece: \( f(x) = -2x + 5 \).

Step2: Substitute \( x = -5 \) into the function

Substitute \( x = -5 \) into \( f(x) = -2x + 5 \):

$$ f(-5) = -2(-5) + 5 $$

Calculate \( -2(-5) = 10 \), then add 5:

$$ f(-5) = 10 + 5 = 15 $$

Answer:

\( 15 \)