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notes/education/math/Polynomial Fractions.md
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TODO: Reformat/fact check

  • to find the x intercept, solve the top/numerator of the fraction for x
  • To find the y intercept, it's the constant term on the top over the constant term on the bottom
  • To solve for the vertical asymptote, find the roots of the bottom.
  • To solve for the horizontal asymptote:
    • if the degree of the leading coefficient on the top is greater than the degree on the bottom, y = 0.
    • If the degree on the top equals the degree on the bottom, y = Leading Coefficient of Top / Leading Coefficient of Bottom.
    • If the degree on the top is greater than the degree on the bottom, divide to find the slant/oblique asymptote.

Point of discontinuity

A point of discontinuity is created when you cancel terms out of the top and the bottom, the cancelled term creates a hole in the graph. For example, if you cancelled out x-2, a hole would be created on the graph at x = 2.

To solve for the y coordinate of a point of discontinuity, take the equation after it's simplified, and plug the x coordinate of the PoD into the equation.