Algebra Examples

$f (x) = {\begin{cases} 3 x - 2 & - 1 \leq x < 0 \\ 2 x + 3 & 0 \leq x < 5 \end{cases}$

Step 1

Since the domain of $3 x - 2$ is all real numbers, the domain of this piece of the function is its restriction, $- 1 \leq x < 0$ .

$[- 1, 0)$

Step 2

Since the domain of $2 x + 3$ is all real numbers, the domain of this piece of the function is its restriction, $0 \leq x < 5$ .

$[0, 5)$

Step 3

Find the domain by taking the union of all of the intervals where the function is defined.

$[- 1, 5)$

Step 4