Today we did a warm-up with rational functions. We reviewed graphing and simplifying, and molly wrote up a google-doc on 'steps to graph rational functions.' We also discussed the equation 0/0=0, and pondered whether or not the answer would be 1, or whether it would result in an error on your calculators. We calculated our asymptotes for our warm-up using division to find the end-behavior. We explored rational functions using grapher, and added extra x's on the numerator's using our previous equation's from our warm-ups. We also fooled around with adding 7x, 5x, 12x, etc. and 2x, etc. on the numerator and denominator (respectively) to change the horizontal asymptotes. What we ascertained is that when there is a larger power on the denominator than on the numerator, the end behavior reached closer and closer to 0, regardless of the numerator's behavior. We can find the end behavior of our graphs by using division if the numerator's power is higher than the denominator's power, if the powers are the same then the lead coefficient of the numerator divided by the lead coefficient of the denominator is the horizontal asymptote for the end behavior, and if the power in the denominator is higher than the highest power in the numerator, then the end behavior is y=0. We finished by graphing the functions with all of the above information. We then calculated f(x) is less than or equal to 0. We used molly's steps to solve and graph our second equation. We revised our steps by adding that you can cancel portions of equations if it is possible. We changed our equation from g(x)=(2-x)(2+x)/(x-2) =-x-2, x does not equal 2. Mr. O'Brien went over what to expect for the test, and gave us the revision problems for the test, and encouraged us to do extra problems if we wanted to. Mr. O'Brien corrected the notion that Juniors will be in class on the 17th when the Supercorrections are due, and we spent the rest of the class reviewing any homework problems we wanted to.