OK... what were the 2 things?
What were the 2 sentences?
|These guys are functions.|
|Graphs hug asymptotes.|
Let's do some graphing, baby!
The y-intercept: Find f(0)
The x-intercept: Set numerator = 0 and solve
Vertical asymptotes: Set denominator = 0 and solve
Now we're ready to graph... Remember that plotting points is for sissies, so use your brain!
First, let's get our intercepts and asymptotes on the graph:
|*Remember the the graph CANNOT cross the y-axis anywhere else and it CANNOT cross the x-axis at all!|
Now, we use our brains and our sentences...
These are the three neighborhoods that this graph lives in:
Let's look at the left neighborhood:
*Remember your 2 sentences!
Since he's a function (and must pass the vertical line test), he can't do both.
What did we say about crossing the x-axis for this guy? (Look back if you need to.)
Yep -- he's not allowed to cross the x-axis! But, look at that bottom guy:
But, he's not allowed to -- so, he's got to live upstairs!
We can use the same reasoning for the right neighborhood:
What about the middle neighborhood?
And remember, he's not allowed to cross the x-axis! So, he CAN'T do any of these things:
(You already have all the pieces!)
Hey, you can check it on the graphing calculator! Enter it in like this: