Precalculus Examples

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

Step 1

Identify the piece that describes the function at $x = 6$ . In this case, $x = 6$ falls within the interval $x > 5$ , therefore use $- x$ to evaluate $f (6)$ .

$f (x) = {\begin{cases} - \frac{2}{5} x - 3 & x < 5 \\ 2 & x = 5 \\ - x & x > 5 \end{cases}$

Step 2

The function is equal to $- x$ at $x = 6$ .

$f (x) = - x]_{x = 6}^{}$

Step 3

Evaluate the function at $x = 6$ .

$f (6) = - (6)$

Step 4

Multiply $- 1$ by $6$ .

$f (6) = - 6$