SOLUTION: 5. a) Determine the equation of the oblique asymptote of y=2x^2-3x+5/3x+2. b) Determine a rational function that has an oblique asymptote of y=3x-1 . Verify this using alge

Algebra ->  Rational-functions -> SOLUTION: 5. a) Determine the equation of the oblique asymptote of y=2x^2-3x+5/3x+2. b) Determine a rational function that has an oblique asymptote of y=3x-1 . Verify this using alge      Log On


   



Question 1037235: 5. a) Determine the equation of the oblique asymptote of y=2x^2-3x+5/3x+2.
b) Determine a rational function that has an oblique asymptote of y=3x-1 . Verify this using algebra.
c) Determine the equation of the parabolic asymptote of
y=3x^3-x^2+4x+1/x-2 .
d) Determine a rational function that has a parabolic asymptote of
y=-x^2+2x-3. Verify this using algebra.

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Try to create a simple example for question d. Degree two, plus simple rational function of degree one. Combine them into a single rational expression.

This would have degree three numerator but degree one denominator.
-x%5E2%2B2x-3%2B2%2F%28x%2B1%29, some original function to have oblique asymptote shaped like a parabola (degree two).

Skipping the algebra steps, this would be
highlight%28%28-x%5E3%2Bx%5E2-x-1%29%2F%28x%2B1%29%29
What happens if you were to perform this as a DIVISION? You'd obviously get back the expression began with, the remainder being 2%2F%28x%2B1%29 which approaches 0 for x to either extreme, and only the concave downward parabola expression persists.

That is just one possible example.