Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Evaluate the function at $x = 2$ .

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

Step 4

Subtract $4$ from $2$ .

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

Step 5

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

$f (2) = - 1 \cdot 4$

Step 6

Multiply $- 1$ by $4$ .

$f (2) = - 4$