Calculus Examples

$f (x) = {\begin{cases} x + 2 & x \leq 2 \\ x^{2} & x > 2 \end{cases}$

Step 1

Find the domain.

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Step 1.1

Since the domain of $x + 2$ is all real numbers, the domain of this piece of the function is its restriction, $x \leq 2$ .

$(- \infty, 2]$

Step 1.2

Since the domain of $x^{2}$ is all real numbers, the domain of this piece of the function is its restriction, $x > 2$ .

$(2, \infty)$

Step 1.3

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

$(- \infty, \infty)$

Step 2

List the domain and range of the piecewise.

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

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

Step 3