- #1
Lizardjuice7
- 5
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Homework Statement
Use the given information about the asymptotes of a function to write an equation for a rational function. You may leave your function in "factored" form.
Homework Equations
1. Vertical Asymptote at x=3 and x=-2
2. Vertical Asymptote at x=5, Horizontal Asymptote at y=3
3. Hole at (2,3), Horizontal Asymptote at y=0
4. Horizontal Asymptote at y=0, Vertical Asymptote at x=6, Goes through the point (3,-2)
5. Vertical Asymptote at x=2, Oblique Asymptote with Equation y=3x-5
The Attempt at a Solution
I know the basics for finding horizontal, vertical, and oblique asymptotes when you have the equation. I'm just having a hard time going backwards.
1. f(x)=1/(x-3)(x+2)
2. f(x)=3x/(x-5)
3. I know the denominator has to be a higher degree than the numerator, bu the "hole" in the graph through me for a loop. No idea where to start.
4. I'm having a similar problem, I don't know how to find a point that goes through the asymptote.
5. f(x)=3x2-11x+10/(x-2)
I got that by setting the denominator equal to zero to find '(x-2)'. I then multiplied the oblique asymptote 'y=3x-5' by '(x-2)' to get the numerator. I think i did something wrong though.
Any help would be greatly appreciated!
Thanks
Lizardjuice7