From 9926ccd9184e775739903f53850d81dd58469fa1 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Thu, 11 Jan 2024 10:31:52 -0700 Subject: [PATCH] vault backup: 2024-01-11 10:31:52 --- education/math/Polynomial Fractions.md | 13 +++++++++---- 1 file changed, 9 insertions(+), 4 deletions(-) diff --git a/education/math/Polynomial Fractions.md b/education/math/Polynomial Fractions.md index 42de521..0301e53 100644 --- a/education/math/Polynomial Fractions.md +++ b/education/math/Polynomial Fractions.md @@ -1,8 +1,13 @@ -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 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 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 -A point of discontinuity is created when you cancel terms out of the top and the bottom, the cancelled t \ No newline at end of file +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. \ No newline at end of file