Basic Terms for Functions

• domain: all possible x values
• range: all possible y values
• x-intercepts/roots/zeros: where a function intersects the x-axis (where y = 0)
• y-intercept: where a function intersect the y-axis (where x = 0)
• vertex/minimum point/maximum point: the point on a quadratic function where it stops increasing and starts decreasing (the maximum point), or where it stops decreasing and starts increasing (the minimum point).

Polynomial Function Basics

A polynomial function is any function in the form ax^n + bx^(n-1) + cx^(n-2) + ... d

• n is a positive integer (1, 2, 3, etc)
• a, b, c, d, etc, can be any number
• the graph of a polynomial function will be smooth (no sharp corners) and continuous (you can draw it in one pencil stroke, without lifting your pencil off the page)

Types of Polynomial Functions

• constant: 0th degree (x^0), straight horizontal line
• linear: 1st degree (x^1), horizontal line in any direction
• quadratic: 2nd degree (x^2), parabolic shape
• cubic: 3rd degree (x^3)
• quartic: 4th degree (x^4)
• quintic: 5th degree (x^5)

Local Minimum Points and Local Maximum Points, and How to Find Them Using a Graphing Calculator

• local minimum point: the lowest point among points near it (but not the function's absolute minimum)
• local maximum point: the highest point among points near it (but not the function's absolute maximum)

Behavior of Even and Odd Degree Functions

Multiplicity of a Root

• multiplicity: how many times a root is repeated
• in other words, the power that a root is to