Here are a few study tips on how to approach the workload of MAT 130:
- Preview the chapter before class. Maybe try a couple homework problems or briefly look through the book for an idea of what you’ll being doing in class. This way you already know whether or not you’re going to have difficulty with the material and you can ask helpful questions.
- Do the homework assignments in parts. Don’t try to sit down and do the entire thing in one sitting unless you’re a rock star on the subject, you’ll wear yourself out. This also means that you should start early. If the homework is due on a Friday, try it for the first time on Tuesday, stop when you get worn out and then go back Thursday and finish. Trust me, I’ve seen a lot of people (including myself) drive themselves crazy trying to sit down and do entire assignments in one sitting.
- Don’t get behind. Doing the assignments in parts and keeping up with everything will save you a ton of time come exam and in-class quiz time because you’ve been practicing.
- Use the “View An Example” tool in MYLABSPLUS homework. This feature is a GEM and if you don’t believe anything else I say all quarter, believe that!
Here are just a few quick tips to help you all navigate the homework for 2.1 and 2.2.
Intercepts: The x-intercept is where the graph crosses the x-axis OR what x is when y is 0, thus the y-value in the ordered pair is ALWAYS 0!! The same thing applies for the y-intercept– x-value in the ordered pair is ALWAYS 0!! When dealing with intercepts, one of the values is always 0 however, both can be 0 if the intercept is at the origin.
Domain & Range: The domain of a graph is all of the exes on that graph, usually written in interval notation. The range of a graph is all of the y-values on that graph, also written in interval notation. If you are given a set of ordered pairs instead of graph, then you will simply list all of the x values as the domain and all of the y values as the range, this is usually not done in interval notation.
Is it a function?: If an “x” occurs more than once, it is not a function. If you graph two points that have the same “x” the graph would not pass the vertical line test and thus, it is not a function. See how that ties together?
Evaluating Functions: f(x) is the function. When given something like f(-2), “-2” becomes x. Rule of thumb: whatever is in those parenthesis is going to replace x in the equation.
Ex: f(x)= -2x+4
This also means that f(-x), simply means replace the exes in the equation with “-x”. Try not to over-think this concept.
Ex: f(x)= -6x+12
-12 = 6x
-2 = x
The concept of the function “–f(x)”, can be a little a tricky but once again don’t over-think. -f(x) literally reads as the “opposite of f(x)”, so just switch the signs.
Ex: f(x)= -24x+36
Identifying Functions: Think of f and g as the name of the functions. Ignore all the fancy notation and do what comes naturally. Applying these symbols is not very difficult, it’s identifying them that’s the hard part.
(f +g)(x) = f(x) +g(x) —-> Just add the functions together.
(f/g)(x) = f(x)/g(x) —-> Just divide the functions.
(f-g)(x) = f(x) – g(x) —-> Just subtract the functions.
Even and odd functions can be a little tricky when you’re first introduced to them but I am going to try to simplify them below.
Remember the functions that we’ve been evaluating the last couple of weeks? When given f(x) you have to evaluate it for f(-x) or -f(x), etc. This is where understanding those concepts comes into play. To find out whether a function is even, odd, or neither, you literally do the exact same thing we’ve been doing except once you’ve evaluated the function you check to see if it’s equal to the original f(x).
If f(x)=f(-x), then the function is an even function
If f(x)=-f(-x), then the function is an odd function
Here’s an example:
Is the following function even, odd, or neither? f(x)=2x+4
*Test the function using the even formula: f(-x)*
Does -2x+4 = 2x+4?
No, so we know that the function is not even.
Now that we know the function isn’t even, is it odd? Does -f(x)=f(-x)?
Does -2x+4 = -2x-4?
No, thus the function is not odd.
Please do not over-think this concept, you all know how to do these problems. Just remember which formula is even vs. which is odd and you will do fine. Remember, we are only building on material that you all learned how to do in the previous section.
Here is a compilation of images that I think will help with the midterm review.
Videos and Handouts
Short & Sweet Explanation of Inverse Functions
Calculating Growth Rates