SOLUTION: Find the vertical asymptote of the rational function f(x)=3x-12/4x-2. Thanks.

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Question 44651This question is from textbook
: Find the vertical asymptote of the rational function f(x)=3x-12/4x-2.
Thanks. This question is from textbook

Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
An asymptote is an imaginargy line on a graoh that plots points where the value of the function is impossible to determine. A verticle asymptote on an x-y graph would have a line equation of the form x=_.
Let's look at your function:
f%28x%29=%283x-12%29%2F%284x-2%29
We know that it is impossible to divide something by zero. Try it on your calculator. You will get some kind of error message.
So the asymptote of the function f(x) must occur when the denominator is equal to zero:
4x-2=0
4x=2
x=2%2F4
x=1%2F2
So the verticle asymptote of f(x) is x=1/2.
Note on the graph below that it is impossible to determine the value of y when x=1/2.
graph%28+300%2C+200%2C+-6%2C+5%2C+-15%2C+15%2C+%283x-12%29%2F%284x-2%29%29+
I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
Adam