Calculus Examples

$f (x) = {\begin{cases} 4 x & x < 0 \\ - 4 x & x \geq 0 \end{cases}$

Step 1

Find the domain.

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Step 1.1

Since the domain of $4 x$ is all real numbers, the domain of this piece of the function is its restriction, $x < 0$ .

$(- \infty, 0)$

Step 1.2

Since the domain of $- 4 x$ 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.

$(- \infty, \infty)$

Step 2

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

$(- \infty, 0)$

Step 3

List the domain and range of the piecewise.

Domain: $(- \infty, \infty)$

Range: $(- \infty, 0)$

Step 4