1. 3-2 Limits
Day 2

2. Anyone figure out the short cut?
That’s right. You look for the overall high power.
Overall High Power in top = Limit dne
Overall High Power in bottom = Limit is 0
High Power in top and bottom are the same
=Limit is where A and B are the high power
coefficients.

3. Why all this trouble
Why are we learning limits? We are getting into another graphing section. We will be graphing Rational Functions (i.e. Ratios of polynomials). These functions won’t be strictly linear or quadratic; instead, they will be functions that act one way near the “center” of the graph and another way as x gets very big or very small. OR they will be linear/quadratic functions with a hole in them.
Why? Because somewhere on these graphs there are x values that just aren’t allowed.

4. Huh??? To get an idea of what we might see, lets go back to Graphcalc
So, you can see that the graphs have these vertical and horizontal lines that act as boundary lines. These are called Asymptotes. Each graph has 2 possible kinds of asymptotes.

5. Asymptotes
Vertical Asymptotes (VA): Restriction of the function (i.e. what would make denominator equal zero)
Hole: Restriction of the function that cancels out.
Why does it still count if it goes away?
Because even if it disappears, it still is a restriction of the original function.
Horizontal Asymptotes (HA): Limit of the function as x .

6. Step 1 – Find Vertical and Horizontal Asymptotes

7. Step 2 - Plot 3 points on each side of the vertical asymptote(s).