## Determining where a function increases, decreases, and is constant 17. Difference quotient and Average rate of change

Concept Notebook

It has been my experience that if a student can explain important concepts in mathematics, they perform and understand on a much higher level than other students. Mathematics can be explained in four different ways: verbal (or written), algebraically, graphically, and using data, lists, or tables.

A list of concepts can be found on our canvas webpage for you to use throughout the semester. You will need to do the following for each concept:

1. Explain each concept in your own words. Please use complete sentences. 2. Doone(orboth)ofthefollowing:
2. Support each concept with a visual representation. This is to be done neatly and clearly showing how that concept is to be used.

b.Support each concept with an algebraic example from your text, notes, or homework. This is to be done neatly and clearly showing how that concept is to be used.

Please use three-ring, loose-leaf, notebook paper. DO NOT use a spiral notebook. Write using complete sentences and only on one side of your paper. Staple your concept notebook. Use a cover sheet that I have put on our canvas webpage before turning it in. Make sure you completely fill out the cover sheet before turning this in.

1. Longdivisionwithpolynomials
2. Synthetic division with polynomials
4. Solutiontoanequation
5. Extraneous solutions
7. Symmetrywithrespecttothex-axis
8. Symmetrywithrespecttothey-axis
9. Symmetrywithrespecttotheorigin

10.Review of all the formulas pertaining to linear equations.

11.Midpoint formula

12.Distance formula

13.Functions and function notation [i.e.. F (x) = y]

14.How do you determine whether an equation is a function or not? [You may want

to include both the vertical line test and an algebraic explanation.] 15. Domain

16.Determining where a function increases, decreases, and is constant 17.Difference quotient and Average rate of change

18.Even and odd functions

19.The important functions we discussed in class (you do not need to include the

greatest integer function). Please leave room for two more important functions

for later

20.How do you graph the piecewise function

21.Horizontal shifting of a function

22.Vertical shifting of a function Reflections about the x – axis

23.Reflections about the y – axis

24.Vertical stretching

25.Vertical shrinking (compressing)

26.Operations on functions

27.Explain the steps you would take to set up a mathematical model for solving

story problems in general