Equations of the basic graphs
| Equation | Graph name |
|---|---|
| y = x^2 | Parabola |
| xy = 1, y = \frac{1}{x} | Rectangular hyperbola |
| y = |x| | Absolute value |
| x^2 + y^2 = r^2 | Circle |
| \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 | Ellipse |
| \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 | Hyperbola |
| y = a^x | Power function |
For the rectangular parabola:
- as x \to \pm \infty, y=0
- as x \to 0, y \to \pm \infty
For the ellipse:
- a and b are positive numbers
- -a \le x \le a
- -b \le y \le b
- if y=0, then x = \pm a
- if x=0, then y = \pm b
For the hyperbola:
- a and b are positive numbers
- y is undefined when -a < x < a
- if y=0, then x = \pm a
- as x \to \infty, y = \pm \frac{bx}{a}
Asymptotes
An asymptote is a line (not necessarily horizontal or vertical) which a curve approaches as x \to \infty or y \to \infty.