I have added a bunch of resources that I think are helpful for MAT 130 students below. 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, Winter 2016
[box]Tuesday 1:30am-2:30pm, Richardson Library 105
Thursday 4:30-5:30pm Richardson Library 105
Office Hour – Wednesday 4-5pm, Richardson Library 111[/box]
Can’t attend any of my sessions? Check out other MAT 130 SI leaders’ schedules here.
Who Am I?
Hi, I’m Faeza and I will be your Supplemental Instructor for this course. As the Supplemental Instructor I will hold two review sessions a week to help you guys prepare for your quizzes, homework, tests, projects, etc. My office hour is a time when you have a quick question you want to ask me.
A little bit about me: I have a bachelor’s degree in math from DePaul and am currently a grad student studying Secondary Education. I will hopefully graduate this June! I’m hoping to meet you guys in my sessions and get to know you better as students.
Here are some resources from Winter 2016
How to do Well in MAT 130
- Attend Lecture – There’s no saying this enough. We cover new topics everyday in lecture so missing even one day can mean you are losing 5% of the information. It also shows the professor that you are trying.
- Do all of the homework – Not only will this prepare you for your online quizzes, it will also help prepare you for your in class quizzes. Remember to take breaks while doing the homework as well. A ten minute break if you’ve been doing an hour of math homework can be really refreshing and helps prevent you from cramming just to get it all done.
- Read! – I can’t stress this enough! If you use the “Show me an example” button on MyLabsPlus please make sure to read what the program says instead of just blindly looking at numbers. Reading the passage of why certain steps are being taken which will help you understand the “why” and “how” of every problem. Comprehend as much as you can.
- 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 your class to help build your math comprehension! It will help you study for your in class quizzes and you can learn from others.
Happy Valentines Day!
I hope you all recognize some of our parent functions!
Finding the Domain:
- If you have a fraction, the bottom of the fraction can never be zero! So set your denominator equal to zero and solve for your variable.
- If you have a square root, remember that what’s under the square root can only be positive or zero, so set the inside of the root to greater than or equal to zero.
- If you have a square root on the bottom of the fraction then remember that the domain can only be positive so set the bottom of the fraction to just greater than zero.
- Remember that a function is even if f(x)=f(-x) or otherwise known as being symmetric with respect to the y-axis. There are a couple ways to solve a problem to determine if it’s even. You can graph the equation and see if its symmetric with respect to the y-axis or plug in a number for x, such as 2, and then plug in the opposite of x, such as -2. Does the equation give you the same output? If yes, then it’s even.
- Remember that a function is odd if f(x)=-f(x) or otherwise known as being symmetric with respect to the origin. Again, you can graph an equation and check for symmetry or just plug in a number x, and its opposite -x. Are the two outputs negative of each other? If yes, its an odd function.
- Also, remember that a function does not have an absolute maximum if its going off into infinite nor an absolute minimum if it’s going down to negative infinite.
Average Rate of Change
The equation of average rate of change should look familiar to you all if your coming straight out of an algebra class because average rate of change is simply the slope of your secant line equation! Therefore your average rate of change equation should be change in y over change in x
Domain and Range
And always remember your domain is the set of all x-values and your range is the set of all y-values. So if you’re given a graph, for the domain look from the left to the right for what your lowest and highest x-values are. To find range, look down to up to find what your lowest y-value to your highest y-value.
Exponents and the Number “e”
What you guys really need to know about the number is that e is approximately equal to 2.718, but you should always use the button on your calculator when calculating anything to do with e. If you’re really curious to know where e comes from here are a couple definitions that use calculus to define it.
But you guys don’t need to worry about that for at least another quarter. Here’s a more useful picture for you guys in case you forgot any of your exponential rules.
These tips apply for solving exponential equations without using logarithms.
1. Make sure to always have the same base on either side of the equal sign! This is key if you want two exponents to equal each other. If the bases are the same and our equation equals each other that means the power must also be the same.
2. Next set the powers equal to each other and solve for whatever your x is.
3. Sometimes the bases won’t automatically be given to you as the same value. In that case make sure you can turn each base into the same base. For example 4 can be written as 2 to the power of 2
[box]From Math Jokes 4 Mathy Folks:
In the expression x3, what do you call the 3? An exponent.
In the expression y2, what do you call the 2? A y‑ponent.[/box]
If you don’t understand what a log is, it’s just the inverse of an exponential function. That’s why a lot of times when we want to solve log equations we first convert things into exponential equations.
How do you convert a log into an exponential? Here’s a fun gif that shows you how to do it:
Since logs and exponential functions are inverses of each other, their graphs are reflected across the y=x axis. The graph in blue is the exponential function while the graph in red shows the inverse log function. Notice that the domain of the exponential function is the range of the log, and the range of the exponential function is the domain of the log function.
Like exponentials, logs also have a lot of properties that you guys should know. Here’s a little reference sheet of the three most common properties used:
Come to the sessions and we’ll discuss how these properties are used when trying to solve log equations.
Word Problems on Financial Models and Exponential Growth
If you need more help with financial models come to SI and we can discuss them some more.
Here are some formula’s you should know for any future quizzes/tests
Using these equations you can also solve for P to find out the principal amount placed in the bank.
Remember the definition of a polynomial is just: where the a’s are real numbers and the exponents of the variables are positive integers, ie, 0,1,2,3…
Here are a couple of examples of what a polynomial is and isn’t:
The two on the left are not polynomials because the first one has a negative exponent, and the second one is a fraction and thus is not considered a polynomial.
If we’re given zeroes of a polynomial, ie, zero: -3, 4, 5 multiplicity 2 then that asks us to turn this into a polynomial written as:
because if we set f(x)=0, then set each factor to zero we’ll get our answers of -3,4, and 5. The multiplicity 2 with the five means that 5 is a zero twice in our polynomial. It also means that if we graph our function, our factors with odd multiplicities cross at the zero’s whereas factors with even multiplicities touch at the zero.
Here’s a link to a fun fact about polynomials: Descarte’s Rule of Signs
If you don’t remember what a rational function is, its just a function f(x)=p(x)/q(x) where p(x) and q(x) are both polynomials and q(x) does not equal 0. It sounds complicated, but they’re the same types of functions we saw in chapter 2.1.
Asymptotes are just a line or curve that a graph of a function approaches but never touches. Vertical asymptotes are easy, because that’s just finding where the denominator does not equal zero. Horizontal asymptotes are a bit trickier.
We learned how to find them in class using limits, but here’s another way that you can do them that you might find easier:
Some useful tips for financial models:
- Identify if you’re going to use the simple interest formula, compound interest, or compound continuously formula.
- If the problem says something like “compounded quarterly” or “compounded monthly” then you will have to use the compound interest formula
- Usually if a problem asks to use the compounded continuously formula, then the word continuously will appear in the problem
- Identify what numbers go to what variables! Remember r=rate (almost always stated as a percentage) n=number of times compounded, t=time or how long will the money stay in the bank?, P= initial amount put into the bank, and A= amount of money that you receive after the certain amount of time.
- Note, time is always in years! So if you ever see a problem that says you only want to keep the money in the bank for 6 months, then that is half a year so you would put in t=1/2
- Also, your variable n should never be a fraction. So even if you read that your money will be compounded quarterly, n=4.
If you need a refresher on how to approach these problems, here’s one of my favorite math tutorial guys on the internet showing you the rational root test: (His name’s PatrickJMT if you ever want need to search for more tutorial video’s in the future)
Graphing Rational Functions
Some helpful video’s if your struggling with Chapter 5 material!
- Composition of functions: https://www.youtube.com/watch?v=S4AEZElTPDo
- Domain of a composition of functions: https://www.youtube.com/watch?v=_zy7Uro7iCg
- Finding inverses: https://www.youtube.com/watch?v=Ec5YYVxyq44
- Exponential Functions: https://www.youtube.com/watch?v=M6f6dANVyxA
- Graphing exponential equations: https://www.youtube.com/watch?v=ls78_2UBcdY
5.5: Properties of logs