Precalculus Examples

$f (x) = {\begin{cases} 2 x - 6 & 0 \leq x < 5 \\ - 1 & x = 5 \\ - {(x - 6)}^{2} & x > 5 \end{cases}$ Find $f (5)$

Step 1

Identify the piece that describes the function at $x = 5$ . In this case, $x = 5$ falls within the interval $x = 5$ , therefore use $- 1$ to evaluate $f (5)$ .

$f (x) = {\begin{cases} 2 x - 6 & 0 \leq x < 5 \\ - 1 & x = 5 \\ - {(x - 6)}^{2} & x > 5 \end{cases}$

Step 2

The function is equal to $- 1$ at $x = 5$ .

$f (x) = - 1 (]_{x = 5}^{})$

Step 3

Evaluate the function at $x = 5$ .

$f (5) = - 1$