Question

consider the following piecewise-defined function.
$f(x) = \

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

$
step 1 of 3: evaluate this function at $x = -2$. express your answer as an integer or simplified fraction. if the function is undefined at the given value, indicate \undefined\.
answer 2 points
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$f(-2) = \underline{\quad\quad}$ $\circ$ undefined

Explanation:

Step1: Determine the applicable function

For \( x = -2 \), we check the conditions. The first part of the piecewise function is defined for \( x \leq -2 \), so we use \( f(x)=\frac{3}{4}x + 3 \).

Step2: Substitute \( x = -2 \) into the function

Substitute \( x=-2 \) into \( \frac{3}{4}x + 3 \):
\( \frac{3}{4}(-2)+3 = \frac{-6}{4}+3 = \frac{-3}{2}+3 = \frac{-3 + 6}{2}=\frac{3}{2} \).

Answer:

\(\frac{3}{2}\)