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$f(x)=\

$$\begin{cases} -\\frac{2}{3}x - 3 & \\text{for } x < -3 \\\\ x + 4 & \\text{for } -3 \\leq x \\leq 1 \\\\ -(x - 3)^2 - 2 & \\text{for } x > 1 \\end{cases}$$

$
find $f(1)$

Explanation:

Step1: Identify correct function piece

Check which interval $x=1$ belongs to: $-3 \leq x \leq 1$, so use $f(x)=x+4$.

Step2: Substitute $x=1$ into the function

<Expression>
$f(1) = 1 + 4$
</Expression>

Step3: Calculate the result

<Expression>
$f(1) = 5$
</Expression>

Answer:

5