Do i use SIN, COS, or TAN to find the missing lengths?
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The y asymptote in a function refers to the horizontal asymptote, or the horizontal line that function generally does not go through. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is the x axis, or y = 0. If the degrees in the numerator and denominator are the same, then the asymptote is y = 1. If the degree in the numerator is higher than the degree of the denominator the asymptote is oblique, or a straight line. I am going to attempt to attach a graph with an asymptote of y = 0 ( the degree of the numerator is less than the degree of the denominator) and one with an oblique so you can see the difference. There are also vertical asymptotes, but that's another concept.
or
is very easy to graph.
Choose whatever value of and use the same for
in the same coordinate. Repeat and strike a line through all the points.
Some examples of valid points would be: ,
,
and
.
Then, to graph you have to look at it in terms of the equation of a line (
) and its parts.
In this case, and
.
So, you choose any value for and you solve to find its
counterpart.
I will start with :
Now, we have a first coordinate: .
Repeat with a different value:
It gives us the coordinates .
Plot those into the graph and strike a line through them.
Wherever the two lines in your Cartesian Plane cross, that is the solution for both equations. It should be .
You can check it by replacing and
by "3" in both formulas and equating the values of
:
Your solution is worked out and checked to be correct.
PS: I am attaching a picture of the graph, so you can have a visual idea of what it should look like.
