This chapter introduces relations and functions. Functions will be the focus of most of the rest of algebra, as well as pre-calculus and calculus. This chapter is an important stepping stone to the rest of algebra.
The first section deals with the difference between relations and functions. It explains how to represent relations and functions using both mapping diagrams and graphs. It also explains how to determine whether or not a relation is a function, given a representation of that relation.
The second section deals with domains of functions and relations; that is, the set of values which are inputs for a relation or function. It explains how to determine the domain of a relation. It also deals with two types of restricted domain--restrictions of an infinite set of numbers, and restrictions of a few points. Some functions cannot take certain values as inputs, and this section details how to find those values.
The final section deals with ranges of functions and relations. While domain is the set of inputs of a function, range is the set of outputs. Both are important to mention when describing a graph or function.
Much of Algebra II and Calculus is concerned with the study of the properties of functions. Here, the student will graph functions, find their maximum and minimum values, and determine their attributes solely from their equations. Functions will be used to solve many different types of problems. However, one must first learn the basics--how to recognize a function, and how to determine its domain and range.
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