Piecewise Function Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy

Evaluate

f(x) = \begin{cases} x^2 & x < 0 \\ 2x + 1 & x \geq 0 \end{cases}

x = -3

x = 0

, and

x = 4

Solution

1
For $x = -3$ : since $-3 < 0$ , use $f(x) = x^2$ . So $f(-3) = (-3)^2 = 9$ .
2
For $x = 0$ : since $0 \geq 0$ , use $f(x) = 2x+1$ . So $f(0) = 2(0)+1 = 1$ .
3
For $x = 4$ : since $4 \geq 0$ , use $f(x) = 2x+1$ . So $f(4) = 2(4)+1 = 9$ .

Answer

f(-3)=9,\; f(0)=1,\; f(4)=9

In a piecewise function, the domain is partitioned into intervals, each with its own rule. The key skill is identifying which interval the input belongs to before applying the corresponding formula.

About Piecewise Function

A piecewise function is defined by different formulas on different non-overlapping intervals of its domain, with the applicable formula determined by the input value.

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More Piecewise Function Examples

Example 2 medium

Determine whether [formula] is continuous at [formula].

Example 3 easy

Given [formula], evaluate [formula], [formula], and [formula].

Example 4 hard

Find the value of [formula] so that [formula] is continuous at [formula].

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Related Concepts

Function Domain Absolute Value Step Function Intuition