1. Piecewise Functions and Limits

2. Objectives I can write equations for graphed piecewise functions
I can write limits for graph end behavior in Limit Notation

3. REMEMBER that piece-wise functions are made up of different functions over various domains
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4. Piecewise-Defined Functions
A piecewise-defined function is composed of two or more functions.
f(x) =
3 + x, x < 0
x2 + 1, x 0
Use when the value of x is less than 0.
Use when the value of x is greater or equal to 0. x y 4 -4
open circle
closed circle
(0 is not included.)
(0 is included.)
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Piecewise-Defined Functions

5. Yesterday we graphed these functions.
TODAY we will work backwards and write the equations from the graph

6. FIRST, we need to identify the equation from transformations

7. Writing Equations from Graphs

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10. SECOND, we need to identify the Domain Restrictions for each piece

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14. Limits and limit notation.
Limits are used to describe the end behavior of a graph.
Question: As you substitute x values approaching a set number into to the function, do the f(x) or y values approach a number? That is, does it have a limit?

15. End Behavior: VERBALLY
As x approaches
f(x) increases without
bound.
f(x) decreases without

16. Limit Notation: also used to show end behavior

17. End Behavior: LIMIT NOTATION

18. End Behavior: LIMIT NOTATION

19. End Behavior: LIMIT NOTATION

20. Homework WS 1-9 Quiz next class
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