tangent

tangent has a function y=Atan(Bx+c)+D. tangents are undefined at 90 and 270 degree. has asymptotes at pi/2 and 2pi/2. the period of tangent graph is pi/B. cotangent occurs at asympyotes of tangent graph. i dont understand how to calculate the vertical asymptotes of tangent graphs.

Sine and cosine

Sine is using the opposite side dived by the hypotenuse. Cosine is using the adjacent side divided by the hypotenuse.  When we solve a triangle, it is really helpful to use sine cosine and tangent.  When we draw a graph for sine and cosine, the basic equation is y=ASine or Cosine (Bx+C) 

Where A is the amplitude of the graph. To get the period of the graph, we use the formula 2pi/B.  If we need to know the phase shift, we set Bx+C equals to zero and solve for x.  It is the same for both sine and cosine graph.   

chapter 3 summary

In chapter three, we learned about rational zeros, rational functions, divisions and asymtopes.  The chapter was not extremely hard to me, it is just a little tidious when doing some steps.  When we are given a function and a zero or factor, we use division to find the other zeros. The power of the first x term indicates the number of zeros.  When the problem asks me to complete the factorization, I divide all the given zeros or factors to get the equation into x square form. We need to put the answer into the form of q(x)•d(x)+r(x).  I liked this chapter eventhough I think I did bad on the test.  

Rational functions

Rational functions are a polynomial over a polynomial. It looks really complicated,but when we take it down into pieces, it is actually easy to graph.   In order to graph the functions, we need to find three things. First, the horizontal,slant and vertical asymtopes, secondly, holes, if the graph has any. To find the vertical asymtopes, we set the denominator to zero and solve for x. To find the horizontal one, we have to test if the value of n is larger than m, if it is, there's no horizontal asymtopes. If n<m! the answer would be y=an/bm. If they are equal, the answer is y=0.  We divid the functions using long division I order to find the slant asymtopes. It only exists if n>m.  We factor and cancel to find the holes, and the answer should be a ordered pair. 

zeros of function

in order to find the zeros of  function, we can use long divition and find the complete factorization. We use the given fator to find the complte factorization. fist we have to test weather or not the given number is a factor. After we find the complete factorization, we can use the quadratic formula to find the zeros. If the answer involves with a negative square root, we have to use imagery numbers to express the answer. I think the problems with the imagery numbers are hard for me, it is really easy to make mistakes during the calculations. I did not understand the problems which they give you multiplicities and zeros, and ask me to find the function.

Piecewise functions

Piece wise function is a function composed with different pieces of different functions. The piece wise function could be continuous or discontinuous. Continuous means that there is no >or <, no gaps in the graph! and can be drawn without lifting the pencil. When graphing a piecewise function, we draw a open circle for >and<, we draw a solid dot for less than or equal to and greater than or equal to. When we have a greatest integer function, expressed with [[x]], the function goes on the same wit a pattern.  The piecewise functions with absolute values flips the results and it looks weird.... This chapter is kind of hard but fun. 

The F(x) man

The project was using the different equations and translating them in order to "kill" all he bad guy.The project was really fun! The reflection section was hard for me. My favorite superhero isCaptain Abs, because he kills a lot of targets at one shot.  The project helped me to practicetranslating equations. When I was doing the reflection part I forgot to put the - sign outside of the equation several times. The equation was wrong when I did it, but I fixed it later.