Definitons

**Definitions**

 * Asymptote**- An approximation for values of the function as they approach +/- infinity. (As in, as the function approaches +/- infinity it will approximate, but never equal, the value of the asymptote.) Most asymptotes are linear, vertical and horizontal, but they are also able to be skew and curved.


 * Domain** - All values that are valid inputs for the function.

2. On a 2-dimensional graph, a function must pass the vertical line test. 3. Functions may be represented by graphs, equations, tables of values, coordinates, by mapping, etc.
 * Function-**1. Description of a relationship in which each input (regardless as to whether it is a single variable or set of coordinates) has exactly one output.


 * Range -** All values that are outputs for the function

Remember: the quadratic formula is the solution to an equation where the relation is equal to 0. In other words, you are finding the intersection of x=0 and the relation or y=0 and the relation.\
 * Roots** - Points in the function where the function intercepts or is tangent to the x/y axis


 * Secant** - a line that intersects a function at two or more points; results in an average rate of change


 * Tangent** - a line that intersects a function at exactly a single point in a defined locality (within a restricted domain); results in an instantaneous rate of change


 * Family of lines** - a group of lines that share the same slope (k(ax + by + c = 0)) or share a common point (eg. all the lines have an output of 4 when the input is 3)

When the discriminant is greater than 1, the solution yields two real and distinct roots. [2 intersections] When the discriminant is equal to 0, the solution yields two real and equal roots. [1 intersection] When the discriminant is less than 0, the solution yields (a) imaginary root(s) [no points of intersection]
 * Discriminant** - the value of b^2 - 4ac for the general quadratic form ax^2 + bx + c = 0.


 * Continuity-** relation lacking gaps (empty subsets)


 * Period -** the time for one complete cycle to take place. (The inverse of frequency, cycles/second)


 * Amplitude -** The maximum magnitude that the waveform varies. Two types of amplitude are commonly used. There is peak-to-peak, in which the amplitude is measured as the difference between the maximum and minimum of the wave. There is also peak-to-mid, in which the amplitude is measured from the midpoint of the wave to the maximum or minimum of the wave.