Precalculus Examples

$f (x) = {\begin{cases} - {(x - 1)}^{2} - 3 & x < 3 \\ - 4 & x = 3 \\ - 3 & x > 3 \end{cases}$ Find $f (8)$

Step 1

Identify the piece that describes the function at $x = 8$ . In this case, $x = 8$ falls within the interval $x > 3$ , therefore use $- 3$ to evaluate $f (8)$ .

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

Step 2

The function is equal to $- 3$ at $x = 8$ .

$f (x) = - 3 (]_{x = 8}^{})$

Step 3

Evaluate the function at $x = 8$ .

$f (8) = - 3$