Precalculus Examples

$f (x) = {\begin{cases} - {(x + 6)}^{2} + 4 & x < - 3 \\ 2 x + 2 & - 3 \leq x \leq 2 \\ - \frac{3}{2} x + 5 & x > 2 \end{cases}$ Find $f (- 4)$

Step 1

Identify the piece that describes the function at $x = - 4$ . In this case, $x = - 4$ falls within the interval $x < - 3$ , therefore use $- {(x + 6)}^{2} + 4$ to evaluate $f (- 4)$ .

$f (x) = {\begin{cases} - {(x + 6)}^{2} + 4 & x < - 3 \\ 2 x + 2 & - 3 \leq x \leq 2 \\ - \frac{3}{2} x + 5 & x > 2 \end{cases}$

Step 2

The function is equal to $- {(x + 6)}^{2} + 4$ at $x = - 4$ .

$f (x) = - {(x + 6)}^{2} + 4 (]_{x = - 4}^{})$

Step 3

Evaluate the function at $x = - 4$ .

$f (- 4) = - {((- 4) + 6)}^{2} + 4$

Step 4

Simplify each term.

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Step 4.1

Add $- 4$ and $6$ .

$f (- 4) = - 2^{2} + 4$

Step 4.2

Raise $2$ to the power of $2$ .

$f (- 4) = - 1 \cdot 4 + 4$

Step 4.3

Multiply $- 1$ by $4$ .

$f (- 4) = - 4 + 4$

Step 5

Add $- 4$ and $4$ .

$f (- 4) = 0$