Find the Domain f(x)=-3x if x<=0; 3x+3 if x>0

$f (x) = {\begin{cases} - 3 x & x \leq 0 \\ 3 x + 3 & x > 0 \end{cases}$

Step 1

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

$(- \infty, 0]$

Step 2

Since the domain of $3 x + 3$ is all real numbers, the domain of this piece of the function is its restriction, $x > 0$ .

$(0, \infty)$

Step 3

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

$(- \infty, \infty)$

Step 4