Rational Functions of the Form f(x) = ax+b / cx+d

For this part, we will focus more on how to find the horizontal asymptote of the function.

The equation of the horizontal asymptote can be found by dividing each term in both the numerator and denominator by x and investigating the behaviour of the function as x approaches to positive or negative infinity.

Short cut to find the horizontal asymptote of the function:

The equation of the horizontal asymptote is same as the coefficient x in the numerator divided by the coefficient s in the denominator.

Thus, horizontal x is a/c.

Isn't it way way easier than dividing each term by x?

NOTES:

• The coefficient b acts to stretch the curve but no effect on the asymptotes, domain or range.
• The coefficient d shifts the vertical asymptote.
• The two brances of the graph of the function are equidistant from the point of intersection of the vertical and horizontal asymptotes.

Source: 

McGraw-Hill Ryerson Advanced Functions 12