Function Rules, Tables, and Graphs

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

Relations and Functions Part 2

Today We Discussed:

We expanded our discussion about relations and functions today and 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:   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 function notation?
2) How do you find f(x) if given a value for x?

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?

Relating Graphs to Events

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 next Tuesday.  

Sections Covered in Textbook:

5-1: Relating Graphs to Events

Resources & Tutorials:

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

Probability of Compound Events

Today We Discussed:

Today we discussed probability of compound events.  We reviewed what the word "compound" means (and in this case, it simply means more than one), and discussed the different types of compound events.  There are two types:  independent events and dependent events.  Independent events occur when the outcome of one event has no effect on the other (ex:  flipping a coin twice).  Dependent events occur when the outcome of the first event does have an effect on the event that comes after (ex:  taking a card from a deck of cards and keeping it, then taking another card).

The numeric probability of dependent events can be found by multiplying the theoretical probability of each event together.

For two independent events, P(A and B) = P(A) * P(B)
For two dependent events, P(A then B) = P(A) * P(B after A)

Vocabulary: independent events, dependent events

Sections Covered in Textbook:

4-6: Probability of Compound Events

Resources & Tutorials:

1) What are compound events?
2) How to determine if your events are independent or dependent.
3) How to find probability of independent events.
4) How to find probability of dependent events.

Applying Ratios to Probability

Today We Discussed:

Ratios can be used to express everyday activities, and we will be using them in the context of probability.  Probability simply is the chance that an event can occur.  We defined all of the terms associated with both theoretical and experimental probability, and talked about how to find a sample space and how that relates to probability.  Exploring experimental probability is a good way to demonstrate that what we expect to happen, does not always occur, and probability is just based upon how likely something is to occur, not a guarantee it will occur.

We will be investigating experimental probability more thoroughly in the next week.


Graphic Credit:  Online Math Learning

Vocabulary: probability, outcome, event, sample space, theoretical probability, experimental probability 

Sections Covered in Textbook:

4-5: Applying Ratios to Probability (pages 211-217)

Resources & Tutorials:

1) What is probability?
2) What is an outcome?
3) What is a sample space? 
4) How do you find the probability of a simple event?
5) What is experimental probability?
6) Math is Fun - Probability (not a video)

Percent of Change

Today We Discussed:

We continued the topic of percents in the context of percent of change.  We can have a positive percent of change (representing an increase) or a negative rate of change (representing a decrease).  To determine the percent of change, we have to compare how much something changed to its original quantity.  Percent of change is relative to the original value.

Vocabulary: percent of change, percent of increase, percent of decrease

Sections Covered in Textbook:

4-4: Percent of Change (pages 204-209)

Resources & Tutorials:

1) What is the percent of change?
2) How do you find percent of change?
3) How do you determine percent of increase or decrease?