asymptotes

G

Guest

Guest
Is there a horizontal asymptote when you have a graph of a function which is an opening upward parabola? Also, do exponential functions always have vertical asymptotes? Having a real hard time with asymptotes.
 
Horizontal asymptotes generally require rational functions (polynomial fractions) with denominator having a degree no smaller than that of the numerator. Does a quadratic, ax<sup>2</sup> + bx + c, qualify?

Vertical asymptotes generally occur where the denominator of a function is undefined. On what basis do you conclude that exponential functions, things of the form f(x) = ab<sup>2</sup>cx</sup>, have vertical asymptotes?

Eliz.

. . . . .FreeMathHelp Lesson: Asymptotes

. . . . .off-site lesson
 
Hi Eliz
Exactly what I'm asking. I've been out of school for twenty years, I'm playing catch up. Please don't mind the dumb questions but I'll take your answer to mean that quadratic functions don't have horizontal asymptotes and exponential functions don't qualify for vertical asymptotes.

Thanks
 
Since "ax<sup>2</sup> + bx + c" has no denominator (of any degree, let alone of degree 2 or greater), then, no, a quadratic cannot have a horizontal asymptote.

Since exponentials are defined everywhere and have no denominators, then, no, they cannot have vertical asymptotes.

The lessons in the links may help you get a better feel for the topic.

Eliz.

P.S. Don't be shy about asking "dumb" questions.
1) Heaven knows, I've asked my share of them. :roll:
2) As long as you show some effort, you'd be amazed how helpful the tutors here can be. :wink: :D
 
You must log in or register to reply here.
Top