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# End Behaviour Of Functions

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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-> -∞ =