Precalculus Examples

$f (x) = {\begin{cases} - 3 x + 9 & 1 \leq x < 5 \\ - 3 & x = 5 \\ - {(x - 7)}^{2} & x > 5 \end{cases}$ Find $f (1)$

Step 1

Identify the piece that describes the function at $x = 1$ . In this case, $x = 1$ falls within the interval $1 \leq x < 5$ , therefore use $- 3 x + 9$ to evaluate $f (1)$ .

$f (x) = {\begin{cases} - 3 x + 9 & 1 \leq x < 5 \\ - 3 & x = 5 \\ - {(x - 7)}^{2} & x > 5 \end{cases}$

Step 2

The function is equal to $- 3 x + 9$ at $x = 1$ .

$f (x) = - 3 x + 9 (]_{x = 1}^{})$

Step 3

Evaluate the function at $x = 1$ .

$f (1) = - 3 \cdot 1 + 9$

Step 4

Multiply $- 3$ by $1$ .

$f (1) = - 3 + 9$

Step 5

Add $- 3$ and $9$ .

$f (1) = 6$