As we discussed in class that for something to be a rational function it is a polynomial over another a polynomial.
usually when dealing with rational functions we are asked to find the x intercepts, y intercepts, vertical asymptotes, and the horizontal asymptotes.
So first we're going to look for the x and y intercepts. To find the x intercepts you simply plug in 0 for y to solve for x. Let's do that!
So if we do this problem out to find the x intercepts, we add 4 to the other side which gives us 4 = 4x we then divide by 4 and we get 1 = X
Our x intercept is (1, 0)!!
To find the y intercepts it's the same process just reversed. To find y we plug in 0 for x to solve for y.
Here on top we get -4 and on the bottom we get 3.
Our y intercept is (0, -4/3)!!
Now that we have our x and y intercepts we can move on to find the asymptotes.
To find the vertical asymptote you want to set the denominator equal to 0!
in doing so we get that the vertical asymptote is x = -3!
To find the horizontal asymptote it becomes a bit harder. To find these you want to set the X's to large numbers, preferably one billion. Now these seem scary because they are big numbers but it's really fairly simple when you get down to it.
By doing the math here it comes about to be about
4 billion / 1 billion then we divide and cancel and come out with 4 for the horizontal asymptotes.
When we graph our function on our graphing calculators or any other graphing machine hopefully you will get something that looks like this:
These do not show the asymptotes so I edited a version on photoshop that should show the vertical asymptotes:
Hopefully this has helped!!!!! At the bottom are a few videos that may explain this if you're a little foggy on some things! See you all in class!
