1.4 KiB
1.4 KiB
- 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.
- if the degree of the leading coefficient on the top is less than the degree on the bottom,
| 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.
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.