Topics for December 5th

Today We Discussed:

Today we took a quiz that covered interpreting graphs, relations, domain and range, functions and graphs. 

For the second part of class we looked at domain and range of graphs, and determining their elements by reading a graph.  We also talked about whether each graph represented a function.  Students will be expected to know the domain and range of functions for the rest of Algebra I, and this topic will be prevalent in Algebra II.

Domain: All Real Numbers

Range:  y <= 2

This is a function!

Sections Covered in Textbook:

No new sections were covered today.

Resources & Tutorials:

1) Find the domain and range from a graph

Assignments:

1) Finish Domain and Range of Graphs Worksheet if not finished in class.
2)  **Planning Ahead** - Chapter 5 Test Next Thursday, December 12th.

Topics for December 4th

Today We Discussed:

We continued our discussion about functions and explored how to write a function rule (basically this is an equation) from a table of values or a graph of coordinate points.  When we move deeper into linear functions, finding the slope, and graphing, we'll take a look at how to deduce a function rule that involves more than one operation.

Sections Covered in Textbook:

5-5: Writing a Function Rule (pages 254-260)

Resources & Tutorials:

1) How do you write a rule from a table? 
2) Finding the function rule from a table (more complicated examples).

Assignments:

1) Writing a Function Rule worksheet
2)  Quiz Tomorrow over Relating Graphs to Events, Relations, Functions, and Graphs

Topics for December 3rd

Today We Discussed:

We expanded our work on functions today with an exploration of graphing.  We discussed three different ways to view a function (as an equation, as a table, and as a graph).  We played around with linear, absolute value, and quadratic functions.

One aspect of functions that is nice is that we can pick what values to use for our domain, and this is especially helpful when dealing with functions containing fractions.  We can pick numbers for the domain that multiply to give us whole numbers, to make our graphs easier to draw.  I will continue to reinforce to students to choose wisely when picking values for the domain.

We also discussed the generic shapes of the three types of functions we talked about.  Linear functions will create a line; absolute value functions will generate a "V"; quadratic equations will generate a "U" or what is called a parabola. 

Vocabulary: independent variable, dependent variable

Sections Covered in Textbook:
5-3: Function Rules, Tables, and Graphs (pages 247 - 252)

Resources & Tutorials:

1) How do you graph a linear function using a table?
2)  Graph an absolute value function from a table.
3)  Graph quadratic function from a table.
4) 6 Mini-Coordinate Planes for Graphing

Assignments:

1) Function Rules, Tables, and Graphs Worksheet
2)  Planning ahead - Quiz Thursday over graphs and functions.

Topics for December 2nd

Today We Discussed:

Welcome back, students!  I hope everyone had a relaxing and fun break!

Today we reviewed what relations are, and reinforced 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 is 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?

Assignments:

1) Functions and Relations Worksheet
2)  Planning Ahead:  Quiz Thursday covering graphs, relations, and functions.

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!

Topics for November 20th

Today We Discussed:

We began our next unit on functions and graphs.  Today we related graphs to real events, by analyzing graphs that relate to time passing.  The shape of the graph can tell a story of what is happening as time passes.

For graphs in general, we will be talking about independent and dependent variables.  Time is considered an independent variable with other variables dependent upon it.



Projects are due tomorrow.  Check yesterday's blog for a list of all items that should be included.  NO LATE PROJECTS will be accepted.

Sections Covered in Textbook:

5-1: Relating Graphs to Events

Resources & Tutorials:

1) Relating Graphs to Events
2) Relating Graphs to Events - another video

Assignments:

1) Pages 238-240 #'s 1-9 all; 12, 14, 16, 18-22 all
2) Projects due TOMORROW!

Topics for Novemer 19th

Today We Discussed:

We used today's class to finish our discussion about probability, and to work on finishing projects.  All students are encouraged to type their conclusions using Google Docs.  Reminder, the finished project should include the following items:

• Rubric
• Printout of Data from 3 Trials of Rolling Dice
• Summary of Trial Data
• Frequency Tables (4)
• Theoretical Outcomes
• Histogram Containing 3 Trials
• Histogram of Trial Averages vs Theoretical Outcomes
• ThinkSheet
• Written Conclusion (Typed preferred)

Sections Covered in Textbook:

None

Resources & Tutorials:

1) Project Packet (if needed)
2) Discussion Questions (if needed)

Assignments:

1)  All corrections & missing assignments due tomorrow.
2)  Project Due TOMORROW!