Calculus Examples

$f (x) = {\begin{cases} x + 1 & - 9 \leq x < 3 \\ - x + 4 & x > 3 \end{cases}$

Step 1

Find the domain.

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Step 1.1

Since the domain of $x + 1$ is all real numbers, the domain of this piece of the function is its restriction, $- 9 \leq x < 3$ .

$[- 9, 3)$

Step 1.2

Since the domain of $- x + 4$ is all real numbers, the domain of this piece of the function is its restriction, $x > 3$ .

$(3, \infty)$

Step 1.3

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

$[- 9, 3) \cup (3, \infty)$

Step 2

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

$(- \infty, 4)$

Step 3

List the domain and range of the piecewise.

Domain: $[- 9, 3) \cup (3, \infty)$

Range: $(- \infty, 4)$

Step 4