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education/math/Polynomial Fractions.md
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TODO: Reformat TODO: Reformat/fact check
- To find the y intercept, it's the constant term on the top over the constant term on the bottom - To find the y intercept, it's the constant term on the top over the constant term on the bottom
- to find the x intercept, solve the top for x - to find the x intercept, solve the top/numerator of the fraction for x
- To solve for the vertical asymptote, find the roots of 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. - 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 ## Point of discontinuity
A point of discontinuity is created when you cancel terms out of the top and the bottom, the cancelled t 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.