1.2: Pre-Cal Review.

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Presentation transcript:

1.2: Pre-Cal Review

Find f(-2), f(1), f(2) and f(3) They don’t need to be able to trace or graph a piecewise but they need to be able to find the y-value and which function to use at any point. This will be crucial to their success in continuity and differentiability.

Answer the following questions about the graph These are just a beginner I have found is good for when we start limits next week.

How many different kinds are there? What is an asymptote? They need to identify vertical and horizontal asymptotes. The vertical are probably more important though. Also, another correct answer would be slant asymptotes, however we don’t really speak of them much in calculus. How many different kinds are there?

What is a discontinuity? Discontinuities What is a discontinuity? What kind of discontinuities are there? Jump Discontinuity Removable Discontinuity Jump Discontinuity Infinite Discontinuity

Asymptotes (Discontinuity) There are vertical asymptotes when? Set denominator equal to zero There are horizontal asymptotes when? BOBO BOTN EATS DC is a simple way to find horizontal asymptotes. It stand for BOBO bigger on top y=0 BOTN bigger on bottom none (this is because it has a slant asymptote) EATS DC exponents are the same divide coefficients. I use this same idea to do limits to infinity next week but it needs a little tweeking for that. BOBO BOTSA EATS DC

How do you find a removable discontinuity (hole)? A hole is produced when there is a cancelation of variables in a function. These are very important to identify in limits. College Board uses them a lot. How can you tell where a hole is by looking at a function?

2. Find the horizontal asymptotes Process 1. Find your removable discontinuities (holes) if any. (Factor and cancel) 2. Find the horizontal asymptotes (BOBO BOTSA EATS DC) 3. Find your infinite discontinuity (vertical asymptotes) (set denominator = 0) This is the basic process I use for the kids. It’s easy to remember and you can’t really mess up if you follow the steps in order.

Find the vertical & horizontal asymptotes and the holes in the functions Notice there is no hole. Make sure you draw one in and tell them the calculators won’t show you a hole. Be smarter than your calc.

Find any discontinuities and name them.

Find the discontinuities. Notice the slant asymptote and ask them where the function is approaching as it goes to infinity and negative infinity. This is a key idea for when we do limits to infinity.