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End Behavior of Functions

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  - ∞

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End Behavior of Functions

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  1. End Behavior of Functions Lesson 2.4

  2. Definitions • 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.

  3. Can be found on page 98 • 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.

  4. Exponential Functions:End Behavior of 2x = ∞ = 0

  5. Oscillating Functions • For example, cosine and sine functions DNE DNE

  6. Discrete Functions with Limits • Probability of rolling an 8 with two dice As the limit approaches ∞, it is approaching its theoretical probability, (14%).

  7. End Behavior of power functions!

  8. F(x) = x4 - 10x2 + 9 • Leading term: x4 • Even- both do the same; positive: up!

  9. f(x) = 4x3 - 3x - 3. • Leading term: 4x3 • Odd- different directions; positive- right up, left down!

  10. f(x) = 4 + 8x2 - x4 • Leading term: -1x4 • even: do the same thing; negative: down!

  11. F(x) = -2x5 + 4x • Leading term: -2x5 • Odd- different directions, negative – right down, left up!

  12. Homework Pages 102 – 103 2-14 evens, 18

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