help Please

[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.