From 6f55be249bcf43f423f40879b0f6bc9abd6623f0 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Tue, 16 Jan 2024 09:18:56 -0700 Subject: [PATCH] vault backup: 2024-01-16 09:18:56 --- education/math/Polynomial Fractions.md | 13 ++++++++++--- 1 file changed, 10 insertions(+), 3 deletions(-) diff --git a/education/math/Polynomial Fractions.md b/education/math/Polynomial Fractions.md index 3908401..4ad2b6c 100644 --- a/education/math/Polynomial Fractions.md +++ b/education/math/Polynomial Fractions.md @@ -9,9 +9,16 @@ | 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 | +| 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. \ No newline at end of file +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 | \ No newline at end of file