Question

find f(-9) for this piecewise-defined function.

f(x) = \

$$\begin{cases} 4x + 1 & \\text{if } x \\leq -8 \\\\ -x + 1 & \\text{if } -8 < x \\leq -1 \\\\ \\frac{2}{3} & \\text{if } x > -1 \\end{cases}$$

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

f(-9) = \boxed{}

Explanation:

Step1: Determine the applicable piece

Check which condition \( x = -9 \) satisfies. Since \( -9 \leq -8 \), we use the first piece \( 4x + 1 \).

Step2: Substitute \( x = -9 \)

Substitute \( x = -9 \) into \( 4x + 1 \): \( 4(-9) + 1 \).

Step3: Calculate the value

\( 4(-9) + 1 = -36 + 1 = -35 \).

Answer:

\( -35 \)