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  • 1. End Behaviour of Functions An introduction to limits
  • 2. What do we mean by “end behaviour”?
    • Generally speaking, we are talking about the y-values as x takes on very large positive or negative values
    • A convenient way to write this is with “limit notation”
      • “ the limit as x gets close to infinity”
      • or
      • lim x -> ∞
  • 3. For example
    • Take the line
    • y = 2x – 3
    • What happens to y as x takes on extreme values; what is the end behaviour?
  • 4.
      • lim x -> ∞ =
      • lim x -> - ∞ =
      • What about other functions we have reviewed so far? What can we say about their end behaviour? What are the limits as x -> ∞ and as x -> - ∞ ?
  • 5. Origin moved from (0,0) to (4,-3) y = lim x-> ∞ = lim x-> -∞ =
  • 6. Origin moved from (0,0) to (-3,2) y = lim x-> ∞ = lim x-> -∞ =
  • 7.
    • Origin moved from (0,0) to (-2,2) y =
    • lim x-> ∞ =
    • Why can we not evaluate lim x-> -∞ ?
  • 8. This is a transformation of y = 2 x , 3 units left and 2 units down Y = lim x-> ∞ = lim x-> -∞ =