function help -multiple choice

[maggie0160]

Which of the following functions has a graph with exactly two vertical asymptotes and one horizontal asymptote?

a. f(x) = (x + 1)/(2x + 4)
b. g(x) = 2x/(x2 - 4)
c. h(x) = (x2 + 4x + 15)/(x + 2)
d. F(x) = (x3 - x - 1)/[(x - 1)(x + 2)]
e. G(x) = (x3 )/(x - 4)
f. none of these


can someone help? a friend thought that a is right but i dont trust her....

 

[tkhunny]

You need better friends. Perhaps you sensed that, already.

In order for there to be TWO vertical asymptotes, the denominator must be at least quadratic. A first degree denominator simply will not do.

This leaves only b. and d., assuming x2 means x².

In order to get a HORIZONTAL asumptote, the degree of the numerator must be equal to or less than the degree of the denominator.

This eliminates d., assuming x3 means x³.

Perhaps you can introduce your friend to rational functions?