From 621f4e1954535844e0a905a9e6083bee7c2c1138 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Tue, 16 Jan 2024 09:13:56 -0700 Subject: [PATCH] vault backup: 2024-01-16 09:13:56 --- education/math/Polynomial Fractions.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/education/math/Polynomial Fractions.md b/education/math/Polynomial Fractions.md index b10b7bd..3908401 100644 --- a/education/math/Polynomial Fractions.md +++ b/education/math/Polynomial Fractions.md @@ -1,4 +1,3 @@ -TODO: Reformat/fact check - 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. @@ -7,6 +6,11 @@ TODO: Reformat/fact check - 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 | ## 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 $x = 2$.