Precalculus Examples

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

Step 1

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

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

Step 2

The function is equal to $- {(x - 4)}^{2}$ at $x = 6$ .

$f (x) = - {(x - 4)}^{2}]_{x = 6}^{}$

Step 3

Evaluate the function at $x = 6$ .

$f (6) = - {((6) - 4)}^{2}$

Step 4

Subtract $4$ from $6$ .

$f (6) = - 2^{2}$

Step 5

Raise $2$ to the power of $2$ .

$f (6) = - 1 \cdot 4$

Step 6

Multiply $- 1$ by $4$ .

$f (6) = - 4$