1. Piecewise-defined Functions
Dr. Fowler  AFM  Unit 1-4
Library of Functions;
Piecewise-defined Functions

2. The Square Root Function
Copyright © 2013 Pearson Education, Inc. All rights reserved

3. The Cube Root Function
Copyright © 2013 Pearson Education, Inc. All rights reserved

4. x and y intercepts are both 0.
This means the function is odd and symmetric with respect to the origin.
x and y intercepts are both 0.
Copyright © 2013 Pearson Education, Inc. All rights reserved

5. The Absolute Value Function
Copyright © 2013 Pearson Education, Inc. All rights reserved

6. x and y intercepts are both 0.
This means the function is even and symmetric with respect to the y-axis.
x and y intercepts are both 0.
Copyright © 2013 Pearson Education, Inc. All rights reserved

7. Copyright © 2013 Pearson Education, Inc. All rights reserved

8. Copyright © 2013 Pearson Education, Inc. All rights reserved

9. Copyright © 2013 Pearson Education, Inc. All rights reserved

10. Copyright © 2013 Pearson Education, Inc. All rights reserved

11. Copyright © 2013 Pearson Education, Inc. All rights reserved

12. Copyright © 2013 Pearson Education, Inc. All rights reserved

13. Copyright © 2013 Pearson Education, Inc. All rights reserved

14. Copyright © 2013 Pearson Education, Inc. All rights reserved

15. Copyright © 2013 Pearson Education, Inc. All rights reserved

16. Piecewise Functions – “Function in Pieces” https://www. youtube

17. Evaluating Piecewise Functions “a Function in Pieces”
Piecewise functions are functions defined by at least two equations, each of which applies to a different part of the domain
A piecewise function looks like this:
f(x) =
x , x  0
x – 1 , x  0
Domain restrictions
Equations

18. 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. Domain Restrictions - Since 2 is  0, you will only substitute into the second part of the function.
f(2) = 2 – 1 = 1

19. 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

20. Try this example:
Evaluate each piecewise function for x = –1 and x = 3.
3x if x < 0
g(x) =
5x – if x ≥ 0
Because –1 < 0, use the rule for x < 0.
g(–1) = 3(–1)2 + 1 = 4
Because 3 ≥ 0, use the rule for x ≥ 0.
g(3) = 5(3) – 2 = 13

21.  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. 

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

23. Excellent Job !!! Well Done