1. 2-2 Extension Part 2: Piecewise Functions

2. Definition:
Piecewise Function –a function defined by two or more functions over a specified domain.

3. f(x) = What do they look like? x2 + 1 , x  0 x – 1 , x  0
You can EVALUATE piecewise functions.
You can GRAPH piecewise functions.

4. f(x) = Evaluating Piecewise Functions:
Evaluating piecewise functions is just like evaluating functions that you are already familiar with.
Let’s calculate f(2).
f(x) =
x , x  0
x – 1 , x  0
You are being asked to find y when
x = 2. Since 2 is  0, you will only substitute into the second part of the function.
f(2) = 2 – 1 = 1

5. f(x) = Let’s calculate f(-2). x2 + 1 , x  0 x – 1 , x  0
You are being asked to find y when
x = -2. Since -2 is  0, you will only substitute into the first part of the function.
f(-2) = (-2)2 + 1 = 5

6. f(x) = Your turn: 2x + 1, x  0 2x + 2, x  0 Evaluate the following:? -3
f(5) = 12 ?
f(1) = 4 ?
f(0) = ? 2

7. f(x) = One more: 3x - 2, x  -2 -x , -2  x  1 x2 – 7x, x  1
Evaluate the following:
f(-2) = ? 2
f(3) =
-12 ?
f(-4) =
-14 ? ?
f(1) = -6

8.  f(x) = Graphing Piecewise Functions: x2 + 1 , x  0 x – 1 , x  0
Determine the shapes of the graphs.
Parabola and Line
Determine the boundaries of each graph.    
Graph the line where x is greater than or equal to zero.
Graph the parabola where x is less than zero. 

9.   f(x) = Graphing Piecewise Functions: 3x + 2, x  -2
Determine the shapes of the graphs.
Line, Line, Parabola
Determine the boundaries of each graph.        

10. Graphing Piecewise Functions
Domain -
Range -

11. Domain -
(-7, 7]
Range -
(-4, -2), [-1, 4]

12. Domain -
[-6, 7]
Range -
[-4, 2], (4, 7)

14. Piecewise Function – Domain and Range
(-6, 7)
[-7, 7]
Range -
[-1, 5 )
(-4.5,
-1],
[0, 4)

15. Domain -
Range -
Domain -
Range -
(-7, -1), (-1, 7]
(-7, 4), [5, 7)
[-1, 5), [6, 6]
[-7, -5), (-2, 7)

16. Domain -
Range -
Domain -
Range -
[-1, 5]
[-5, 3]