We started class with a radical function warm up. After we did this problem, but before we went over it, we went over the quiz for the first half of class, and learned some ways to use our calculators to solve for i or find a complex conjugate. Next we went over the homework problems from two nights ago, on page 179. We went over problems 43 and 47, finding the roots over rational numbers, real numbers, and complex numbers for #43. For #47, we solved by factoring by grouping, then solving for zero. We learned how to factor a number that is the sum of two squares. So (x^2 +25) becomes (x+ 5i) (x-5i), which is the difference between two squares. When a complex number is a root, another root will be the complex conjugate. So since 5i is a root, - 5i is too. After going over those two problems we went back to the warm up. To help solve this problem, we went to http://calc101.com/webMathematica/long-divide.jsp This website can do long division, and it will show you the steps as well. We then went over how to find a slant asymptote. To find the slant asymptote, you can use the form of the radical function where there is and x + c outside of the fraction. To find the y-intercept it is easiest to use the original, unfactored form. All the x values will cancel out, and you will be left with the c values, which have no x value. This is the y intercept. We then talked about a removable asymptote, which is when a factor cancels out of a radical function, but should still be in the domain. For example: (x^2 + 1)(x + 1) ( x-3)/(x-2) (x-1) (x-3) The (x-3) will cancel out, but x cannot equal 3, so you must draw an open circle at this point on the graph.
There is no quiz on Friday, but the Unit 2 test is on Tuesday.