Precalculus Examples

$f (x) = {\begin{cases} - x - 5 & x \neq - 2 \\ - 2 & x = - 2 \end{cases}$ Find $f (- 4)$

Step 1

Identify the piece that describes the function at $x = - 4$ . In this case, $x = - 4$ falls within the interval $x \neq - 2$ , therefore use $- x - 5$ to evaluate $f (- 4)$ .

$f (x) = {\begin{cases} - x - 5 & x \neq - 2 \\ - 2 & x = - 2 \end{cases}$

Step 2

The function is equal to $- x - 5$ at $x = - 4$ .

$f (x) = - x - 5 (]_{x = - 4}^{})$

Step 3

Evaluate the function at $x = - 4$ .

$f (- 4) = - (- 4) - 5$

Step 4

Multiply $- 1$ by $- 4$ .

$f (- 4) = 4 - 5$

Step 5

Subtract $5$ from $4$ .

$f (- 4) = - 1$