Ray’s MAT 130 Resources

Below are a bunch of resources that I think are helpful for MAT 130 students. If you have any questions come to an SI session or leave a comment below. You can also upload any of your helpful resources in the comment section!

My Session Schedule, Spring 2016

[box]Tuesday 2:45-3:45pm, Richardson Library 105

Thursdays 11:45-12:45pm, Richardson Library 111

Office Hour – Thursdays 2:45-3:45pm,  Richardson Library 105

Final Review Session:

Tuesday, June 7th  1:00pm-3:00pm Richardson Library 111


Can’t attend any of my sessions? Check out other MAT 130 SI leaders’ schedules here.

minion-stuart-dance-gif-1445349814n84gkFind practice questions ->here <-minion-stuart-dance-gif-1445349814n84gk

About Me


Hi MAT 130 folks! My name is 泰华, but you can call me Ray and I will be your supplemental instructor for this quarter. As a supplemental instructor, I am here to help everyone to learn efficiently in a smart
way and I aim to help y’all to succeed in this class! I will be hosting two review/study sessions each week starting on week two, and as you might have noticed, I have an office hour on Thursday after class and this is for you to come to ask me quick questions.

A little about me: I have a B.A. in Business Management & a B.A. in Economics, and currently I am working on the M.S. in Predictive Analytics here at DePaul University. 


What are some MAGIC TRICKS to do well in this class?

  • Attend lectures, be on time and ask questions! We cover new material every day in lecture so if you miss 15 minutes or one lecture, you will need to spend approximately twice as much time to catch up. Also remember to ask questions in class so the professor and I will know what you don’t understand.magic-trick-animated-gif-16
  • Do all of the homework by yourself and “Half-an-Hour Rule”. The best way to learn math is through practice questions. If you are struggled with a question, give it half an hour before asking tutors, the professor, me or other fellow classmates. (Trust me, it works…like magic)
  • Read notes/books or watch tutorial videos to preview and review, but watch out for the cat videos (never go there when you are studying). P.S. highly recommend Khan Academy videos.
  • When doing online quizzes, try doing it without using notes. I know that it can be tempting at times to use your notes when doing the online quizzes. I understand that you want a good grade. However, it helps if you do it without your notes so you can know what you do and don’t know.
  • Attend SI sessions. Work with others in the class to help build your math comprehension! It will help you to study for your in-class quizzes and you can learn from others. Also I will be there to study with everyone and I am awesome, so you should be there.

What to bring to the SI sessions?

  • Notes, textbooks, pen/pencil
  • We will create a question bank throughout the SI sessions so bring a piece of paper for each session
  • YOU! (also your friends who are taking the same class)



You can do it!



x: independent variable
y: dependent variable
f(x): function f of x

Finding Domain

  1. Question to answer: what values can [independent variables] be?
  2. If the function has division, find out where the denominator will equal zero.
  3. If the function has a square root, find out where the square root part will have a negative value under the sign.
  4. Combine both of the above qualities to find the domain. For example, if you cannot evaluate at 3 and you cannot evaluate from -4 to 4, then you just make the biggest set —  from -4 to 4 (because 3 is included anyway)

Finding Range

  1. Question to answer: what values can [dependent variables] be?
  2. Find the minimum and maximum of the function vertically


In summary………………

Function Combination

Finding Intercepts

  • To find x-intercepts, set y equal to zero
  • To find y-intercepts, set x equal to zero
  • Example 1: Linear equation

  • Example 2: Quadratic function

Determine Symmetry

  • A graph is said to be symmetric about the x-axis if whenever (a, b) is on the graph then so is (a, -b).  Here is a sketch of a graph that is symmetric about the x-axis.

Screen Shot 2016-04-06 at 11.13.37 PM

  • A graph is said to be symmetric about the y-axis if whenever (a, b)  is on the graph then so is (-a, b).  Here is a sketch of a graph that is symmetric about the y-axis.

Screen Shot 2016-04-06 at 11.15.52 PM

  • A graph is said to be symmetric about the origin if whenever (a, b) is on the graph then so is (-a, -b).  Here is a sketch of a graph that is symmetric about the origin.

symmetric 3

We have some fairly simply tests for each of the different types of symmetry:

  1. A graph will have symmetry about the x-axis if we get an equivalent equation when all the y’s are replaced with y.
  2. A graph will have symmetry about the y-axis if we get an equivalent equation when all the x’s are replaced with x.
  3. A graph will have symmetry about the origin if we get an equivalent equation when all the y’s are replaced with y and all the x’s are replaced with x.

Odd & Even Functions

Test to determine if a function y=f(x) is even, odd or neither: Replace x with -x and compare the result to f(x)

IF f(-x) = f(x), the function is even.

IF f(-x) = – f(x), the function is odd.

IF f(-x) ≠ f(x) and f(-x) ≠ -f(x), the function is neither even nor odd.


Maxima & Minima


Average Rate of Change average rate of change

Graphs of Functions

Basic function graphs

Piecewise-Defined Functions

What are piecewise functions? Combination of several different functions.

WATCH OUT! After multiple functions are combined piece by piece (interval by interval), it still have to be a function. Remember what the function definition is? One independent value (x-value) corresponds to only one dependent value (y-value).

Function Transformation

Function Transformation

***Function stretching, compressing and reflecting tutorial

Completing The Square

Completing the square

Composite Functions

One-to-One Function

Defintion: A function for which every element of the range of the function corresponds to exactly one element of the domain.

Important: A one-to-one function HAS to pass BOTH vertical line and horizontal line tests!!!!!!

Exponential Function

Logarithmic Function

Polynomial Functions

Rational Function

Polynomial & Rational Inequalities



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