How do you find the asymptotes for #f(x)=(5x-15)/(2x+4)#?

1 Answer
Aug 26, 2015

Answer:

This function has a horizontal asymptote at #y=5/2# and a vertical asymptote at #x=-2#.

Explanation:

#f(x)=(5x-15)/(2x+4)# is a rational function where the degree of the numerator and denominator are equal (they're both equal to 1).

Therefore, it has a horizontal asymptote at the value of #y# that is the ratio of the coefficients of the leading terms (highest powers of #x#), which is #y=5/2#.

Since the denominator is zero when #x=-2# and the numerator is not zero there, it also has a vertical asymptote at #x=-2#.