The following is an example of a piecewise function:

Since piecewise functions are made up of "pieces", one property we are interested in is continuity. For example, consider the following: x2 when x ≤ 1 f(x) = 2x - 3 when x > 1

Is this function continuous? Check f(1) of both "pieces":

Example: For what value of b is f(x) continuous? |x| when x ≤ -2 f(x) = √x + b when x > -2

Check f(-2) for both "pieces":

Piecewise Functions

The absolute value function is a piecewise function. f(x) = |x| can be written as f(x) =

Write f(x) = |2x + 4| using piecewise notation.(Hint: Where is the vertex?)

f(x) =

In the exercises you will be asked to state the domain and range of each piecewise function. These should be stated using interval notation.

Examples: Interval Notation x > 3 x ≤ -8 y < 0 4 ≤ y < 7 x Є R