Question

find f(-3) for this piecewise-defined function.

f(x) = \

$$\begin{cases} 6x + 4 & \\text{if } x \\leq -2 \\\\ -5x + 1 & \\text{if } -2 < x \\leq 1 \\\\ 4x + 2 & \\text{if } x > 1 \\end{cases}$$

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

f(-3) = \boxed{\space}

Explanation:

Step1: Determine the applicable piece

We need to find \( f(-3) \). First, check which piece of the piecewise function applies. The value \( x = -3 \) satisfies \( x \leq -2 \), so we use the first piece \( f(x)=6x + 4 \).

Step2: Substitute \( x=-3 \) into the function

Substitute \( x = -3 \) into \( 6x + 4 \):

$$
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$$

Answer:

\( -14 \)