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.