Calculus Examples

$f (x) = {(x + 3)}^{2} - 2$ , $x \leq - 3$

Step 1

Since the domain of ${(x + 3)}^{2} - 2$ is all real numbers, the domain of this piece of the function is its restriction, $x \leq - 3$ .

$(- \infty, - 3]$

Step 2

The range is the set of all valid $y$ values. Use the graph to find the range.

$[- 2, \infty)$

Step 3

List the domain and range of the piecewise.

Domain: $(- \infty, - 3]$

Range: $[- 2, \infty)$

Step 4