Algebra Examples

$f (x) = {\begin{cases} x + 6 & - 5 \leq x < 1 \\ 9 & x = 1 \\ - x + 3 & x > 1 \end{cases}$

Step 1

Since the domain of $x + 6$ is all real numbers, the domain of this piece of the function is its restriction, $- 5 \leq x < 1$ .

$[- 5, 1)$

Step 2

Since the domain of $9$ is all real numbers, the domain of this piece of the function is its restriction, $x = 1$ .

$[1, 1]$

Step 3

Since the domain of $- x + 3$ is all real numbers, the domain of this piece of the function is its restriction, $x > 1$ .

$(1, \infty)$

Step 4

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

$[- 5, 1) \cup (1, \infty)$

Step 5