Reading Quiz – 2.2 In your own words, describe what a “End Behavior Model” is.

Limits involving infinity 2.2

Goal I will be able to define vertical and horizontal asymptotes, and calculate limits to infinity.

Definition

Example

The line y=b is a horizontal asymptote if: or Definition

As the denominator gets larger, the value of the fraction gets smaller. So there is a horizontal asymptote at y=0. Example Find the horizontal asymptote of

Example: Find:

How to find the Horizontal asymptotes Divide the lead terms (ones with the biggest exponent)

Example

You try!

Example

Finding the H.A also gives you the end behavior An End behavior model is a simple function that models what a more complex function does at infinity.

End Behavior Models: Test to check if a function is a end behavior model. A function g is: a right end behavior model for f if and only ifa left end behavior model for f if and only if

Example: Right-end behavior models give us: dominant terms in numerator and denominator

Test of model Our model is correct. Example: As, approaches zero. (The x term dominates.) becomes a right-end behavior model.becomes a left-end behavior model. As, increases faster than x decreases, therefore is dominant. Test of model Our model is correct.

Example 7: becomes a right-end behavior model.becomes a left-end behavior model. On your calculator, graph: Use:

Don’t Forget… You can always look at the graph to see what is happening with the function if you are unsure.

Homework 2.2 AND read pages Reading quiz tomorrow!