October 15, 2008

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting started - Functions.

In this mini-lesson, you'll learn what functions are and understand concepts such as relation, notation, domain and range of a function. Some of the high level definitions of these concepts are being mentioned below -- we suggest you to go through the explanation provided in the video by our instructor. Here are a few high level definitions:

In this mini-lesson, you'll learn what functions are and understand concepts such as relation, notation, domain and range of a function. Some of the high level definitions of these concepts are being mentioned below -- we suggest you to go through the explanation provided in the video by our instructor. Here are a few high level definitions:

- A function is a relation between two sets of values, where the second value (the “output") is uniquely determined by the first value (the "input").
- A relation is a collection of ordered pairs. If the pair has real numbers, e.g. (5, 2), then the relation may be graphed on a pair of coordinate axis and they may satisfy a formula. For example, Set A is all the people in a class and Set B are their height. The pairing of names with corresponding height is a relation.
- If every element of Set A has a unique image in a Set B, then it is a function. E.g., y = f(x) = x
^{2}+ 2, means for every value of x we get a unique value of f(x). If y is completely determined by a quantity x, then y is the function of x, denoted by f(x). For example, the area of a circle with radius r is denoted by f(x) = ?r^{2}. - Domain is all the possible values of x and the range is all the resulting possible values of y.
- A mapping, f: A?B in which each element of set A is the image of at least one element in set B.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Algebra I. Click on the video below to go through it. If you like it, you can buy our online course in Algebra I by clicking here.

- Mathematics > General
- Mathematics > Algebra
- Education > General

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Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.?

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).