To Be or Not to Be.... a Function

In class today we explored the differences between relations and functions and learned about function notation, domain, and range.  Here are the top ten eight take aways from class:

8. A relation is a connection between input values and output values (can be an equation, a table, a graph, a verbal description)

7. A function is a specific type of relation.  In a function, each input value maps to just one output value.  The examples below are from our class worksheet.

6. You can tell if a graph is a function by using the vertical line test.  Does a vertical line intersect the graph in more than one location?  NO: it is a function,  YES: it is not a function

5.  f(x) is function notation.  It reads "f of x" or "f in terms of x."  f(x) is the output of your function, just like y.

4. Every relation and every function has a set of input values and a set of output values.  The set of input values is called the domain.  The sent of output values is called the range.

3.  Tip!  To remember which is which, don't forget that it's alpahbetical:

2. The sets of numbers in the domain and range can be written a few different ways:

• If your domain or range is finite, you can list it inside squiggly brackets, like this:  {x | x = -2, 0, 4 }  (Which relation, on the sheet above and from class, matches with this domain?)
• If your domain or range in infinite, you can represent it with inequalities inside squiggly brackets, like this:

 

(Which function, on the sheet above and from class, matches with this range?)

•  If your domain or range includes all real numbers, you can denote this with:

 

1.  FUNctions!

For a more thorough re-teaching of this topic, you can check out the video below:

This material can also be found in your book, Section 3-10, Relations.