asymptotes for (x^5 - x^4 + ...) / (x^4 - 2x^2 - ...)
- Thread starter ca.chick
- Start date
No different than finding the asymptote of a less-complex rational.
Finding Vertical Asymptotes:
The graph of f(x) has vertical asymptotes at the zeros of the denominator
Finding Horizontal Asymptotes:
The graph of f(x) has one or no horizontal asymptotes determined by comparing the
degrees, (exponents), of the numerator and denominator.
a.) Degree of numerator is less than degree of denominator: Graph has y=0 as
a horizontal asymptote.
b.) Degree of numerator is greater than degree of denominator: Graph has no
horizontal asymptote.
c.) Degree of numerator is equal to degree of denominator: Graph has the first
term of the numerator divided by the first term of the denominator as its
horizontal asymptote.
Finding Vertical Asymptotes:
The graph of f(x) has vertical asymptotes at the zeros of the denominator
Finding Horizontal Asymptotes:
The graph of f(x) has one or no horizontal asymptotes determined by comparing the
degrees, (exponents), of the numerator and denominator.
a.) Degree of numerator is less than degree of denominator: Graph has y=0 as
a horizontal asymptote.
b.) Degree of numerator is greater than degree of denominator: Graph has no
horizontal asymptote.
c.) Degree of numerator is equal to degree of denominator: Graph has the first
term of the numerator divided by the first term of the denominator as its
horizontal asymptote.
- Joined
- Apr 12, 2005
- Messages
- 11,339
Oh, don't be lazy. Factor what you can.
In this case, there isn't much to do in the numerator. There is one Real solution, but it isn't Rational.
The denominator factors nicely. Give it a shot. How many factors of 9 are there?
y-intercept is trivial.
Have a little fun with partial fractions or long division and the oblique asymptote will pop out.
This sort of problem can be a bit of work. It will be very rewarding when you complete it. It will be very overwhelming if someone does it for you.
In this case, there isn't much to do in the numerator. There is one Real solution, but it isn't Rational.
The denominator factors nicely. Give it a shot. How many factors of 9 are there?
y-intercept is trivial.
Have a little fun with partial fractions or long division and the oblique asymptote will pop out.
This sort of problem can be a bit of work. It will be very rewarding when you complete it. It will be very overwhelming if someone does it for you.
- Joined
- Feb 4, 2004
- Messages
- 16,582
Try following the tutor's suggestion: Use long division. This is illustrated in many online lessons, if you are needing worked examples to help you get going.ca.chick said:
Eliz.