Calculus Examples

$f (x) = x^{2} + 1$ , $- 2 < x < 3$

Step 1

Since the domain of $x^{2} + 1$ is all real numbers, the domain of this piece of the function is its restriction, $- 2 < x < 3$ .

$(- 2, 3)$

Step 2

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

$[1, 10)$

Step 3

List the domain and range of the piecewise.

Domain: $(- 2, 3)$

Range: $[1, 10)$

Step 4