Precalculus Examples

$f (x) = {\begin{cases} x + 9 & x < - 5 \\ 2 & x = - 5 \\ - x - 1 & x > - 5 \end{cases}$ Find $f (- 7)$

Step 1

Identify the piece that describes the function at $x = - 7$ . In this case, $x = - 7$ falls within the interval $x < - 5$ , therefore use $x + 9$ to evaluate $f (- 7)$ .

$f (x) = {\begin{cases} x + 9 & x < - 5 \\ 2 & x = - 5 \\ - x - 1 & x > - 5 \end{cases}$

Step 2

The function is equal to $x + 9$ at $x = - 7$ .

$f (x) = x + 9 (]_{x = - 7}^{})$

Step 3

Evaluate the function at $x = - 7$ .

$f (- 7) = (- 7) + 9$

Step 4

Add $- 7$ and $9$ .

$f (- 7) = 2$