help Please

[MCccoy]

Can someone please show me how to :determine the equations of the two asymptotes of the rational function: a) (102*x + 17)/(6*x - 72)
b) 1/(2*x + 16) +18
in the form y=a and y=b.

Your Help would be highly appreciated.
cheers.

[NickThissen]

I can't tell exactly how they want you to do this (I'm going to guess it's part of school work?), but an easy way is often to look what happens if x goes to infinity.

You have to work out the limits properly, but most of the time you can already see what will happen even without the calculation of the limits.
For b for example, if x goes to a very large number, the formula becomes:
1/(very large number + 16) + 18.
Now, a very large number + 16 is just another very large number so that won't matter very much.
Then, you probably know what 1/(infinity) is?
Then you could work out what shape the formula is going to take.
(1/infinity) + 18 = 0 + 18 = 18.
So the asymptote will be y = 18.

Try the other one for yourself.


EDIT
Forgot that you also have to check for -infinity (x goes to a very large negative number).
The calculation is the same, but sometimes the asymptote can be different for + and -..!

[krtxmrtz]

Can someone please show me how to :determine the equations of the two asymptotes of the rational function: a) (102*x + 17)/(6*x - 72)
b) 1/(2*x + 16) +18
in the form y=a and y=b.

Your Help would be highly appreciated.
cheers.

For part a:

The limit of your function when x tends to infinity is 102/6 = 17 so the horizontal asymptote is y = 17 (same value when x tends to minus infinity).

The vertical asymptote occurs when the function goes to infinity, i.e. when the denominator is 0. Therefore: x = 12.

For part b:

The vertical asymptote is x = -8 (the fraction tends to infinity). As for the horizontal one, when x tends to plus/minus infinity the fraction tends to 0 so the function tends to 18. Then the equation is y = 18.