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Warmup: Let’s Practice Graphing Piecewise Functions Ourselves

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Presentation on theme: "Warmup: Let’s Practice Graphing Piecewise Functions Ourselves"— Presentation transcript:

1 Warmup: Let’s Practice Graphing Piecewise Functions Ourselves

2 Example Problem #2

3 Finding Limits Graphically
PRE-CALCULUS UNIT 1 Day 2 Finding Limits Graphically

4 What is a limit? A limit describes how the output values of a function behave as input values approaches some given #, “c” Notation: Read “limit of f(x) as x approaches c is equal to L”

5 Kinds of limits THE Limit (double-sided limit) Left-hand limit
Limit of f(x) as x approaches c from either direction. Only exists if left-hand and right-hand limits are the same. Left-hand limit Limit of f(x) as x approaches c from the left side. Right-hand limit Limit of f(x) as x approaches c from the right side.

6

7 Misconception #1 A function does not have to be defined at “c” in order for the limit to exist.

8 Misconception #2 If a function is defined at “c”, f(c) does not necessarily have to equal L.

9 Two Cases for When the Limit is D.N.E. (Does Not Exist)
Behavior differs from the left and right Oscillating Behavior Ex/

10 Practice

11 Practice

12 Practice

13 Practice 13

14 Draw a graph such that

15 Draw a graph such that

16 Draw a graph such that

17 Draw a graph such that

18 Draw a graph such that

19 Draw a graph such that


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