Precalculus Examples

$f (x) = {\begin{cases} - 4 & 2 \leq x < 6 \\ 4 & x = 6 \\ - {(x - 7)}^{2} & x > 6 \end{cases}$ Find $f (3)$

Step 1

Identify the piece that describes the function at $x = 3$ . In this case, $x = 3$ falls within the interval $2 \leq x < 6$ , therefore use $- 4$ to evaluate $f (3)$ .

$f (x) = {\begin{cases} - 4 & 2 \leq x < 6 \\ 4 & x = 6 \\ - {(x - 7)}^{2} & x > 6 \end{cases}$

Step 2

The function is equal to $- 4$ at $x = 3$ .

$f (x) = - 4 (]_{x = 3}^{})$

Step 3

Evaluate the function at $x = 3$ .

$f (3) = - 4$