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End Behaviour of Functions An introduction to limits
What do we mean by  “end behaviour”? <ul><li>Generally speaking, we are talking about the y-values as x takes on very larg...
For example <ul><li>Take the line  </li></ul><ul><li>y = 2x – 3 </li></ul><ul><li>What happens to y as x takes on extreme ...
<ul><ul><li>lim x ->  ∞ =  </li></ul></ul><ul><ul><li>lim x -> - ∞ =  </li></ul></ul><ul><ul><li>What about other function...
Origin moved from (0,0) to (4,-3)  y =  lim x-> ∞ = lim x-> -∞ =
Origin moved from (0,0) to (-3,2)  y =  lim x-> ∞ = lim x-> -∞ =
<ul><li>Origin moved from (0,0) to (-2,2)  y =  </li></ul><ul><li>lim x-> ∞ = </li></ul><ul><li>Why can we not evaluate li...
This is a transformation of y = 2 x  , 3 units left and 2 units down Y =  lim x-> ∞ = lim x-> -∞ =
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End Behaviour Of Functions

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End Behaviour Of Functions

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

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