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
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