Calculus Examples

$f (x) = {\begin{cases} 1 - x & x \leq - 1 \\ 2 & - 1 = 1 \end{cases}$

Step 1

Find the domain.

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Step 1.1

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

$(- \infty, - 1]$

Step 1.2

Since the domain of $2$ is all real numbers, the domain of this piece of the function is its restriction, $- 1 = 1$ .

$[1, 1]$

Step 1.3

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

$(- \infty, - 1] \cup [1, 1]$

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: $(- \infty, - 1] \cup [1, 1]$

Range: $[2, \infty)$

Step 4