Calculus Examples

$k (x) = {\begin{cases} x + 4 & x < - 1 \\ 5 & - 1 = 2 \end{cases}$

Step 1

Find the domain.

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Step 1.1

Since the domain of $x + 4$ is all real numbers, the domain of this piece of the function is its restriction, $x < - 1$ .

$(- \infty, - 1)$

Step 1.2

Since the domain of $5$ is all real numbers, the domain of this piece of the function is its restriction, $- 1 = 2$ .

$[2, 2]$

Step 1.3

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

$(- \infty, - 1) \cup [2, 2]$

Step 2

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

$(- \infty, 3) \cup [5, 5]$

Step 3

List the domain and range of the piecewise.

Domain: $(- \infty, - 1) \cup [2, 2]$

Range: $(- \infty, 3) \cup [5, 5]$

Step 4