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Pre-Calculus > Tail Behavior
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Tail Behavior

Let's look at the other tail:

graph looking at the eventual behavior of the upward tail ... As x gets smaller and smaller, we are following the graph to the left. As we do this, what's happening to the y values on the graph? 53... 725... 9280... 5,932,491 If Pierre was running on this thing, would he need mountain climbing equipment?

As x gets smaller and smaller, the height of the graph is going up, up, up.

As x approaches-infinity, the height of the graph approaches
infinity.  
Asx --> -infinity , f( x ) --> infinity

To sum up:
 

graph of -x^3+ some x stuff ... as x --> -infinity , f( x ) --> infinity ... as x --> infinity , f( x ) --> -infinity
 

 

 

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Pre-Calculus

  1. Basic Formulas to Know
  2. Horizontal and Vertical Lines Review
  3. Increasing and Decreasing of Functions Review
  4. Logarithms
  5. Maximums and Minimums: Finding Relative Extrema
  6. More On Sideways Parabolas
  7. Piecewise Functions Review
  8. Slopes of Lines
  9. The Difference Quotient Review
  10. The Unit Circle
  11. Equations of Lines
  12. The Pythagorean Identities
  13. Advanced Composition of Functions
  14. Other Identities to Know
  15. Freaky Factoring
  16. Solving Trig Equations
  17. Tangent Lines
  18. Graphs to Know and Love
  19. Shifting, Reflecting, Etc.
  20. Absolute Values
  21. Polynomials
  22. More on Tangent Lines
  23. Tail Behavior
  24. Intro to Rational Functions
  25. Rational Functions - Intercepts
  26. Rational Functions - Vertical Asymptotes
  27. Rational Functions - Horizontal Asymptotes (and Slants)
  28. Rational Functions - The Whole Thing
  29. Rational Functions - Increasing and Decreasing Revisited
  30. Rational Functions - More on Limits
  31. Exponentials and Logarithms