Semester Exam Breakdown

Rational Expressions
Parent Functions
Solving-exponents-logarithms
Radical Expressions (square root thing)
Asymptotes
Inverses
Imaginary numbers
Finding zeros in Quadratic
Simple Interest
Logarithm -using laws to combine and change to exponential

You are going to be allowed a graphing calculator for the final.

FINDING ZEROS IN QUADRATICS
There are several ways to find zeros that we have talked about.

1. Graphing- graph the function and see where the quadratic crosses the x axis
2. Factor-factor the quadratic expression and set the factors equal to zero and solve
3. Use the quadratic formula-it must be set equal to zero

There are always 2 ZEROS!!!!

Parent Functions
For parent functions, you can utilize the general for of transformations:

Compound Interest



Inverses
For invereses, SWITCH THE X AND Y AND SOLVE!!!!!!

Logarithms
Laws of Logs

Conversion from logs to exponential


Asymptotes
We know that there are several graphs that have asymptotes.

1. Exponential - has a horizonatal asymptote at y=0 in the parent function and moves accordingly with the vertical shift of the parent function
2. Logarithmic - has a vertical asymptote at x = 0 in the parent function and moves accordingly with the horizontal shift of the parent function.
3. Rational -  has a horizontal asymptote at y = 0 and a vertical asymptote at x = 0 in the parent function. The INTERSECTION of these two asymptotes moves with the up, down, left and right shifts of the parent function.

YOU can always look for clarification on asymptotes by looking at the graph.

REMEMBER: asymptotes are imaginary lines that create barriers for the function. The function is always discontinuous(has a hole) at an asymptote

Radical Expressions

Rational Expressions

Rational Expressions

For Rational Expressions (fractions with variables), we need to make sure we have a sound foundation in factoring!!!!!!!

For multiplying and dividing rational expressions (we are not solving for x, we are simplifying), we need factor if need be, and cancel or eliminate similar factors on the top and bottom, simplify and we're done!!!!!

WATCH OUT for division!!! You have to flip the expression after the division and then it turns into multiplication.




For adding and subtracting rational expressions we must find a common denominator!!!!!!! Then distribute or foil in the numerator, combine like terms, see if you can factor again in order to cancel out any factors in the bottom and you are done. See the video for a tutorial!!!!



Here are some more notes on adding and subtracting rational expressions...

 

Factoring - Greatest Common Factor, Difference of Squares, Mustang Method, Factor by Grouping

FACTORING

Everyone should have the notes for 5-1 and 5-2. In 5-1 you are to review GCF (Greatest Common Factor), Difference of Squares, Mustang Method and Factoring by grouping.


YOU should remember how to do GCF. All we have to look for is what ALL the terms are divisible by. Whether it be variables, numbers or that leading negative.

Difference of squares we have already talked about. REMEBER: there must be a negative in between the numbers or it will not work.

Mustang Method - If you have three terms AFTER you have completed GCF.

1. Multiply the first term and the last term
2. Factor- find the factors that when added equal the middle term. Go ahead and set up your double parenthesis (x+ factor 1  )(x+ factor 2  )
3. Divide both factors by the number in front of the x squared
4. Reduce the fractions
5. Move any remaining denominators in front of the x's

Factor by grouping - you have already been introduced to this method, but most of you did not like it. So I have attached the notes with directions. You HAVE to use this method when you have 4 terms.

Factoring Quiz Corrections

Information regarding corrections of the Factor quiz:

You need to review the following video Factoring quadratics and write a pragraph reviewing the video in addition to  answer the question, 'This video helped/did not help me rereview factoring and why?' It will need to be typed or scanned and submitted to edmodo by Saturday December 11 at 11:59pm.

How to find the Intersection point of a system in the calculator

PUT IN Y=                                PUT BOTH EQUATIONS INTO Y= IN SLOPE INTERCEPT FORM

PRESS GRAPH                         PRESS THE GRAPH BUTTON

PRESS 2ND TRACE                 PRESS THE 2ND BUTTON AND THEN TRACE

PRESS 5                          

ENTER ENTER ENTER           PRESS 'ENTER' 3 TIMES

Multiplying and Dividing Fractions

While I am thinking about, I want to make sure that everyone is familiar and comfortable multiplying and dividing fractions because it will come in handy here soon. I found a couple of videos I want to share. The short one is this video that talks about some of rules of muliplying and dividing fractions and it's only 2 minutes long. I also found another video that is from Khan academy, and he has done some other videos I have seen. Here are also some follow up problems from Khan for multiplying and dividing fractions that you can do on your own. The Khan links also cover reducing before multiplying which can help you make calculations quicker mentally. Check it out!!!!!!

Substitution video

Ok, So I know some of you like to watch videos, but hate watching boring math instruction videos. We are going to cover solving systems this week and I found this video that hopefully will introduce you to solving systems by substituion. There is also another video about solving systems by graphing. I feel this is one of the better math teachers with videos up on the web so I would appreciate if everyone can at least take a look at both of them before next week. They are both about 8 minutes long so they won't eat up a lot of your computer time. If you want to go visit the website, it is yaymath.org. Unfortunately I am still looking for something about solving systems by elimination. Let me know if you have questions. See you Monday.