Let's do another one:
|The y-intercept: Find f(0)|
|The x-intercept: numerator = 0, solve|
|Vertical asymptotes: denominator = 0, solve|
*When this is the case, we're going to be forced to "quickie plot" a few points to nail the graph. No, this is not being a sissy -- we'll have no choice. Calculus will take care of this though!
OK, let's start graphing!
Let's get our intercepts and asymptotes down:
Since we've got that pesky y = 0 horizontal asymptote, we can't use our "nowhere else" info on the x-intercepts to figure out the "upstairs" or "downstairs" stuff. Until we have Calculus, we're going to have to humble ourselves and plot some points -- kind of! We're going to avoid taking that pathetic trip to Sissyville by cheating a little bit... I call it "quickie plotting."
Four strategically located points will do it and all we really need to know is if he's above or below the x-axis at each point.
We'll be plugging x's into the factored form:
*We only care about positives and negatives -- see if you can do it!
Now we've got it!
|*Remember that he can only cross the x-axis at |
x = 0... So, once he's below, he'll be stuck there... and, once he's above, he'll have to stay above!
(You already have all the pieces!)
*Remember that, when you are working these things out -- write out all of your work in a neat and organized way! This is one of the main reasons you have to take math classes -- they teach you to organize your thoughts AND TO THINK!