end behavior of functions

12
Lesson 2.4

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End Behavior of Functions. Lesson 2.4. Definitions. End behavior: A description of what happens to the values f(x) of a function f as x  ∞ and as x  - ∞ - PowerPoint PPT Presentation

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Page 1: End Behavior of Functions

Lesson 2.4

Page 2: End Behavior of Functions

End behavior: A description of what happens to the values f(x) of a function f as x ∞ and as x -∞

Asymptote: a line that the graph of a function y = f(x) approaches as the variable x approaches a fixed value or increases or decreases without bound.

Page 3: End Behavior of Functions

The behavior of a function as x ∞ or as x -∞ falls into 1 of 3 categories.

1. Values approach real number L

2. The values of f(x) increase or decrease without bound; that is f(x)

∞ or f(x) - ∞

3. The values of f(x) follow neither 1 or 2.

Page 4: End Behavior of Functions

= ∞

= 0

Page 5: End Behavior of Functions

For example, cosine and sine functions

DNE

DNE

Page 6: End Behavior of Functions

Probability of rolling an 8 with two dice

As the limit approaches ∞, it is approaching its theoretical probability, (14%).

Page 7: End Behavior of Functions
Page 8: End Behavior of Functions

Leading term: x4

Even- both do the same; positive: up!

Page 9: End Behavior of Functions

Leading term: 4x3

Odd- different directions; positive- right up, left down!

Page 10: End Behavior of Functions

Leading term: -1x4

even: do the same thing; negative: down!

Page 11: End Behavior of Functions

Leading term: -2x5

Odd- different directions, negative – right down, left up!

Page 12: End Behavior of Functions

Pages 102 – 103

2-14 evens, 18