Precalculus Examples

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

Step 1

Identify the piece that describes the function at $x = - 1$ . In this case, $x = - 1$ falls within the interval $x < 1$ , therefore use $- x - 2$ to evaluate $f (- 1)$ .

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

Step 2

The function is equal to $- x - 2$ at $x = - 1$ .

$f (x) = - x - 2 (]_{x = - 1}^{})$

Step 3

Evaluate the function at $x = - 1$ .

$f (- 1) = - (- 1) - 2$

Step 4

Multiply $- 1$ by $- 1$ .

$f (- 1) = 1 - 2$

Step 5

Subtract $2$ from $1$ .

$f (- 1) = - 1$