Relations and Functions Part 1

Today We Discussed:

Today we explored what relations are, and discussed the concepts of domain and range.  We also defined functions as special relations where there is exactly one range value for each given domain value.  We modeled the different ways of representing a relation:  set of ordered pairs, table, mapping diagram, and graph, and used the vertical line test to determine if a graph is a function or not.  We also discussed why graphs that fail the vertical line test are not functions.

Many students will try to "force" a relation to be a function, or will feel like it is "bad" if a relation is not a function.  We discussed this tendency, and why it's perfectly fine to have a relation that is not a function.  Just because something does not fit a particular definition does not make it bad or good - it just is what it is!

Vocabulary:  relation, domain, range, function, vertical line test, mapping diagram, 

Sections Covered in Textbook:

5-2: Relations and Functions (pages 241-246)

Resources & Tutorials:

1) What is a relation?
2) What is domain?
3) What is the range of a relation?
4) How do you find the domain and range of a relation?
5) What is a function?
6) How do you figure out if a relation is a function?

Relations and Functions

Today We Discussed:

Today we explored what relations are, and discussed the concepts of domain and range.  We also defined functions as special relations where there is exactly one range value for each given domain value.  We modeled the different ways of representing a relation:  set of ordered pairs, table, mapping diagram, and graph, and used the vertical line test to determine if a graph is a function or not.  We also discussed why graphs that fail the vertical line test are not functions.

Many students will try to "force" a relation to be a function, or will feel like it is "bad" if a relation is not a function.  We discussed this tendency, and why it's perfectly fine to have a relation that is not a function.  Just because something does not fit a particular definition does not make it bad or good - it just is what it is!

Finally, we took a look at function notation.  Most students are intimidated by this method of representing an equation in two variables.  They are mostly comfortable with an equation of the form

y = 2x + 3 

We discussed that f(x) = 2x + 3 is just a fancy way of writing the above equation, and it can be described by saying "there is some function that uses the variable x, where the function rule is 2x+3. 

We discussed evaluating functions for given domain values, to produce range values.

DIXI-ROYD was also reinforced today.

Vocabulary:  relation, domain, range, function, vertical line test, mapping diagram, DIXI-ROYD, function rule, evaluate function, function notation

Sections Covered in Textbook:

5-2: Relations and Functions (pages 241-246)

Resources & Tutorials:

1) What is a relation?
2) What is domain?
3) What is the range of a relation?
4) How do you find the domain and range of a relation?
5) What is a function?
6) How do you figure out if a relation is a function?
7) What is function notation?
8) How do you find f(x) if given a value for x?

9) Relations and Functions class notes

Assignments:

1) Functions and Relations Worksheet
2) Dice Project due FRIDAY (7th and 8th)

Topics for November 21st

Today We Discussed:

We began our discussion of relations and functions today.  We will take several days to cover this first section as it contains a lot of new vocabulary, and symbolism that will take some time to get used to.  We discussed what a relation is (set of ordered pairs), what the domain is (inputs) and what the range is (outputs).  We also talked about functions which are just special relations where there is only a single output (range value) for every input (domain value).  We also talked about function rules (an equation that describes a function), and we introduced function notation.

A quick mnemonic to remember what terms are associated together is DIXI-ROYD.  A summary of terms and how they are related is shown in the graphic below.

Vocabulary:  relation, domain, range, function, vertical-line test, function rule, function notation, mapping diagram, DIXI-ROYD

Sections Covered in Textbook:

5-2: Relations and Functions

Resources & Tutorials:

We will pick this discussion back up when we return from Thanksgiving Break.

Assignments:

NONE!  Have a great Thanksgiving Break!