Functions

When we're talking about functions, we're beginning to talk about equations with 2 variables and equations that we can graph. We'll get into the graphing part in Unit 3, but for now let's discuss what a function is and how we can identify it.
 * What is a function?**

A function is an equation with 2 variables (x and y) and whenever you put in a number for x you get one and ONLY ONE y-value out.

For example: y = 2x + 1 IS a function because no matter what number you put in for x, you will only get 1 number out for y.


 * How can I tell if an equation is a function or not?**
 * On the Regents, you may see this question written in 2 different ways. **


 * First, you may be given a set of points (x, y). If there is THE SAME X with A DIFFERENT Y, then it is NOT a function. **


 * Example: (1, 2), (0, -3), (2, 2), (-10, 7) IS a function because there is only 1 y-value that goes with each x-value. **


 * Example: (1, 2), (0, 3), (2, 2), (1, 7) IS NOT a function because there are 2 y-values (2 and 7) for the same x-value (1) **


 * Second, you may be given a set of graphs. You use what is called the VERTICAL LINE TEST to determine if a graph is a function or not. To use the vertical line test, you draw a vertical line through the graph. If it crosses the graph MORE THAN ONCE, the graph is NOT a function. If it crosses the graph EXACTLY ONCE, then the graph IS a function. **

Example: The graph below IS a function because no matter where we draw the vertical line (green) it only crosses the graph once.



Example: The graph below IS NOT at function because the vertical line crosses the graph more than once.



**TASK: Describe in your own words the two methods used to determine if something is a function or not.**

TASK: Open the document below and answer each question. Turn your work in during class.