Precalculus Examples

$f (x) = {\begin{cases} - {(x - 1)}^{2} - 1 & x < 2 \\ - 6 & x = 2 \\ - x + 3 & x > 2 \end{cases}$ Find $f (5)$

Step 1

Identify the piece that describes the function at $x = 5$ . In this case, $x = 5$ falls within the interval $x > 2$ , therefore use $- x + 3$ to evaluate $f (5)$ .

$f (x) = {\begin{cases} - {(x - 1)}^{2} - 1 & x < 2 \\ - 6 & x = 2 \\ - x + 3 & x > 2 \end{cases}$

Step 2

The function is equal to $- x + 3$ at $x = 5$ .

$f (x) = - x + 3 (]_{x = 5}^{})$

Step 3

Evaluate the function at $x = 5$ .

$f (5) = - (5) + 3$

Step 4

Multiply $- 1$ by $5$ .

$f (5) = - 5 + 3$

Step 5

Add $- 5$ and $3$ .

$f (5) = - 2$