Algebra Examples

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

Step 1

Since the domain of $2$ is all real numbers, the domain of this piece of the function is its restriction, $x < 4$ .

$(- \infty, 4)$

Step 2

Since the domain of $- 3$ is all real numbers, the domain of this piece of the function is its restriction, $x \geq 4$ .

$[4, \infty)$

Step 3

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

$(- \infty, \infty)$

Step 4