The first and most important thing for you to learn about Algebra is variables. Variables are any placeholders for something else. In regular Algebra you will learn to use variables to represent numbers in a specific scenario. In early algebra you will mainly use two variables. One will be the independent variable which you change to modify the dependent variable. The most common name or symbol for the independent variable is x, and the most common one for the dependent variable is y. You might change the name of these variables to fit your scenario better. In most textbooks and other practice problems you will see x and y.
A function is anything where combinations of independent variables equal one specific dependent variable. You can prove if it is a function by looking at the inputs (independent variables) and the outputs (dependent variables) If there is more than one output for each input you do not have a function. A function can apply to many things through life, but in this book we will try to focus purely on algebraic functions. You express a function by replacing the dependent variable by f(x) where x is whatever you independent variable is.
Functions can be viewed in many ways the first way you should learn to view functions with is tables. In the table you have one column to tell you what the independent variable is then in the column directly across from that you should have a column telling you what the dependent variable is. To check to see if the values in the table are from a function you would check to see if there is only one dependent variable for each instance of the independent variable. It is not a function if it has more than one dependent value for each instance of the independent variable
Another way to view functions which you will probably use much more is graphs. The easiest way to do this is to use a graphing calculator. If you have a TI-84, a TI-83, or a TI-82 I will explain how to do that here. If you have a TI-Nspire it is explained in the appendix B. If you have any other kinds of calculator check your manual which probably came with it to see how to graph functions. From here on out when I say calculator I am referring to one of the aforementioned TI-80’s. To view a function on a calculator you would turn the calculator on and enter the equation into the space given when you press the Y= button. Once you have done that press the graph button and the function should be displayed. You can get a table on a calculator by pressing 2nd and then pressing graph. Graphs are the easiest things to check to see if they are displaying functions. You just look at it and see if a vertical or straight up and down line would pass through it in more than one place. If that happens then you do not have a function.