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Mathematics - Algebra

Pick a rational function.
Here are some examples you can use:
y = (x+1)/(x-2), y = 3x/(x^2-1),
y = (2x-1)/4x, y = (x+3)/(x^2-1),
y = (x^2+1)/(x^2 -3),
y = (6x+1)/(x^2),
y = x^2/(x-3),
y = (3x-5)/(4x+7),
y = (x^2)/(x^3 - 1)

a) Vertical Asymptote (if any)
b) Horizontal Asymptote (if any)
c) Slant Asymptote (if any)
d) X and Y intercepts

Graph your function.

For all Rational Functions:

*By looking at the equation for a rational function, how can you tell if there will be "y-values" which will never occur?

*If you let x take on very large positive values, and very small negative values, what can this tell you about the far right and left sides of the graph of a rational function that has horizontal asymptotes?

Solution Preview

The solution file is attached with the full response including graphs.

Consider the rational function f(x) = x^3/(x^2 - 4)
The graph of this function is shown below:

Vertical Asymptotes
After canceling any common factors in the numerator and denominator, the remaining denominator ...

Solution Summary

A complete, neat and step-by-step Solution is provided in the attached file to address the rational functions, finding the vertical asymptote, horizontal asymptote, slant asymptote, and X and Y intercepts.