notes/education/math/Polynomial Fractions.md

• to find the x intercept, solve the top 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 less 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.

Value	Instructions	Example
x intercept	Solve the top of the fraction for x	\frac{x-1}{x+2} -> x-1 = 0 -> x_{int} = 1
y intercept	divide the constant term on top by the constant term on bottom	$\frac{3x+1}{2x+2}$-> \frac{3}{2}
vertical asymptote(s)	Set the bottom of the fraction to 0 and solve (find the roots)	\frac{x-1}{x-2} -> x-2 = 0 -> VA = 2
Horizontal asymptote	- if the degree of the leading coefficient on the top is less 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.	- Degree on top is smaller than degree on bottom \frac{x-1}{x^2+2} -> $y=0$ - Degree on top is the same as degree on bottom

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.

Term	Definition
Degree	The power that a variable is raised to. EG, x^5 would have a degree of 5
Leading Coefficient	The number that