Calculus Examples

$f (x) = {\begin{cases} | 3 x | & - 2 \leq x < 0 \\ x^{3} & x \geq 0 \end{cases}$

Step 1

Find the domain.

Tap for more steps...

Step 1.1

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

$[- 2, 0)$

Step 1.2

Since the domain of $x^{3}$ is all real numbers, the domain of this piece of the function is its restriction, $x \geq 0$ .

$[0, \infty)$

Step 1.3

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

$[- 2, \infty)$

Step 2

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

$(0, \infty)$

Step 3

List the domain and range of the piecewise.

Domain: $[- 2, \infty)$

Range: $(0, \infty)$

Step 4