Precalculus Examples

$f (x) = {\begin{cases} {(x + 3)}^{2} - 3 & x < - 3 \\ - 1 & x = - 3 \\ - x - 7 & x > - 3 \end{cases}$ 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 ${(x + 3)}^{2} - 3$ to evaluate $f (- 4)$ .

$f (x) = {\begin{cases} {(x + 3)}^{2} - 3 & x < - 3 \\ - 1 & x = - 3 \\ - x - 7 & x > - 3 \end{cases}$

Step 2

The function is equal to ${(x + 3)}^{2} - 3$ at $x = - 4$ .

$f (x) = {(x + 3)}^{2} - 3 (]_{x = - 4}^{})$

Step 3

Evaluate the function at $x = - 4$ .

$f (- 4) = {((- 4) + 3)}^{2} - 3$

Step 4

Simplify each term.

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Step 4.1

Add $- 4$ and $3$ .

$f (- 4) = {(- 1)}^{2} - 3$

Step 4.2

Raise $- 1$ to the power of $2$ .

$f (- 4) = 1 - 3$

Step 5

Subtract $3$ from $1$ .

$f (- 4) = - 2$