1.9 KiB
1.9 KiB
| 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 Term | The element in the polynomial with the highest degree. EG, in the polynomial 3x^4 + 2x^3 + 5x^2 - 3x + 6, 3x^4 would be the leading term because it has the highest degree. |
| Leading Coefficient | The coefficient of the leading term in a polynomial. For example, if the leading term was 3x^4, the leading coefficient would be 3. |
| Constant Term | The number in a polynomial that is not multiplied by a variable. EG, 7. |