1: Relations and Functions

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1.1: Sets of Real Numbers and the Cartesian Coordinate Plane
A brief refresher on some basic notions is welcome, if not completely necessary, at this stage. To that end, we present a brief summary of 'set theory' and some of the associated vocabulary and notations we use in the text.
- 1.1.1: exercise temp
1.2: Relations
All of Precalculus can be thought of as studying sets of points in the plane. With the Cartesian Plane now fresh in our memory we can discuss those sets in more detail
1.3: Introduction to Functions
One of the core concepts in College Algebra is the function. There are many ways to describe a function and we begin by defining a function as a special kind of relation.
1.4: Function Notation
If we think of the domain of a function as a set of inputs and the range as a set of outputs, we can think of a function f as a process by which each input x is matched with only one output y. Since the output is completely determined by the input x and the process f, we symbolize the output with function notation `f(x) ' . In other words, f(x) is the output which results by applying the process ff to the input x .
1.5: Function Arithmetic
It would seem natural, then, that functions should have their own arithmetic which is consistent with the arithmetic of real numbers. The following definitions allow us to add, subtract, multiply and divide functions using the arithmetic we already know for real numbers.
1.6: Graphs of Functions
In the previous section, we said that one could describe relations algebraically using equations. In this section, we begin to explore this topic in greater detail. The main idea of this section is the graph of an equation is the set of points which satisfy the equation. That is, a point $(x,y)$ is on the graph of an equation if and only if $x$ and $y$ satisfy the equation.
1.7: Transformations
In this section, we study how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas. The transformations we will study fall into three broad categories: shifts, reflections and scalings, and we will present them in that order.
1.E: Relations and Functions (Exercises)
These are homework exercises to accompany Chapter 1 of Stitz and Zeager's "Pre-Calculus" Textmap.

Contributors

Carl Stitz, Ph.D. (Lakeland Community College) and Jeff Zeager, Ph.D. (Lorain County Community College)