Question

Which statement is true if the degree of the numerator's polynomial function is greater than the degree of the denominator's polynomial function?

A. it has one horizontal asymptote
B. it has one vertical asymtote
C. it has no horizontal asymptote
D. it has no vertical asymptote

Answer 1

This subject is on rational functions

Answer 2

don't understand this:/

Answer 3

would it be a?

Answer 4

This can be understood by looking at each choice separately. You could have an expression like x - 9 in the denominator where you would have a vertical asymptote at x = 9. So you can eliminate "d". Or you could have an expression like x^2 + 9 in the denominator, in which case you would not have a vertical asymptote. So, you can eliminate "b". You could have an expression like: (x^2 - 9)/(x + 3) which resolves down to: x - 3 which has no horizontal asymptote, so you can eliminate "a".

Answer 5

ahh i see

Answer 6

So, you could have done the problem the way I did it above, or you could realize that the resultant expression is going to be an expression in "x" where it will behave at least like a linear function (when the power of x in the numerator is only 1 more than in the denominator), or like a quadratic, where it is 2 greater, etc.