## Definition Of Piecewise Function

Piecewise function is a function f(x) defined piecewise, that is f(x) is given by different expressions on various intervals.

### Examples of Piecewise Function

The graph below shows the piecewise function f(x) = |x| if x ≤ 0

= sinx if x > 0

### Video Examples: Piecewise Functions.mov

### Solved Example on Piecewise Function

**Ques: **Choose the graph of the piecewise function f(x) = cosx if x < 0="">

= e^{x} if x ≥ 0

##### Choices:

A. Graph A

B. Graph B

C. Graph C

D. None of these

Correct Answer: B

### Solution:

Step 1: The graph of the piecewise-defined function

f(x) = cosx if x <>

= e^{x} if x ≥ 0 is as shown below. [Use a grapher.]