Precalculus Examples

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

Step 1

Identify the piece that describes the function at $x = 2$ . In this case, $x = 2$ falls within the interval $- 3 \leq x \leq 2$ , therefore use $- x - 4$ to evaluate $f (2)$ .

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

Step 2

The function is equal to $- x - 4$ at $x = 2$ .

$f (x) = - x - 4 (]_{x = 2}^{})$

Step 3

Evaluate the function at $x = 2$ .

$f (2) = - (2) - 4$

Step 4

Multiply $- 1$ by $2$ .

$f (2) = - 2 - 4$

Step 5

Subtract $4$ from $- 2$ .

$f (2) = - 6$