Graphs

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.