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Assignment

Section 4 - 7

Unit 1- Functions and Their Graphs

This unit focuses on the definition of functions, how to graph a function, and the relationship between functions and their graphs.

Follow this link for a list of Graphing Calculator Skills needed for this chapter.


Section 1.1 Graphing

This course utilizes a graphing approach to the material.  This section introduces the the graphing calculator and LiveMath notebooks.  The graphing calculator does more than graph and this course will utilize those features for a better understanding of the mathematics.
Please coordinate this material in the text with the graphing calculator, videos, manual, and the CD ROM.
 It is VERY important to familiarize yourself with the graphing calculator and become comfortable using it on a regular basis. You should print out allpages,including the LiveMath pages.  

See  calculator skills page for more information.
For help with the LiveMath plug-in please click here.


Section 1.2   The straight line

This section is a review of material relating to the straight line. You should be able to:
determine the slope of a line given the equation or given two points
find the equation of a line, given the slope and a point
find the equation of a line given two points on the line

Click on the LiveMath image to explore slope.

discern between parallel and perpendicular lines and find equations using perpendicular and parallel slopes
determine the slope of a line from its graph
apply all of the above to applications

Click on the LiveMath image to explore parallel lines.

Click on the LiveMath image to explore parallel and perpendicular lines.

RE Homework: You should be able to do all the problems, however these assignments are the minimum you should do in order to understand the materials.


Section 1.3  Functions
This section defines a function. A function is a relation ship between pairs of values. This appears in every day life and we will be exploring this topic in this section.  For example, the income taxes you pay to the IRS are related to how much you earn.  The phone bill while staying at a hotel, is related to the number of calls placed.  The profit made by a company is related to the quantity of its product sold.
The main concepts in this section to understand are:
         Domain and range  - non graphical
This is a very important concept and will follow this course through most of the chapters.

Example1. Given the following relation:
{ (2, 4) , (4, 7), ( 2, 8.5)}
The domain is {2, 4} and the range is the set {4, 7, 8.5}

Note: This relation is NOT a function.
To be a function, for each member of the domain , there can be only one member of the range. Here the value 2 has two different values in the range.

Example 2.  Given the relation (function)
y = | x | or f(x) = | x|
The domain is the set of all real numbers, and the range, output, is the set of numbers greater than or equal to zero.

         Independent and dependent variables, value of a function
When a function is given in function notation y = f(x), then x is the independent variable and y is the dependent variable. f(x) is the value of the function at x.

Example 1.      y = f(x) = 3x + 5
f(2) = 3(2) + 5 = 11 is the vlue of the function at x = 2

On the graph,  the value can be seen below.

Example.  In the function d = f(s) = .5s2 - 4s + 6,
s is the independent variable and d is the dependent variable.
f(s) is the value of the function at s.

Click on the icon to explore the value of functions with LiveMath

         Piecewise functions
These are introduced in this section and graphing them on the graphing calculator is defined on page 106. Please graph this type of function is to use the divide symbol "/" instead of using multiplication as shown in the text.

                 Y1=(x2 + 1 )/ (x < 0)

                 Y2= (x -1) / (x > 1)    

Try both ways and see which is easier for you to understand. The symbols >, <,  >, < , and = can be found in the TEST menu ( over the MATH button) on the TI 82/83. If you would like a more detailed explanation of how the calculator graphs piecewise functions, please E-Mail me or post a note on the Webboard.

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Click on the LiveMath image above for interactive exploration of piecewise functions

 

Evaluating functions
This can be easily done or checked on the graphing calculator by entering the function into Y1, exiting to the home screen and using the VARS key, YVARS, to evaluate Y1(a) for some given value "a". This will help in exercises 25-42 when it asks for f(x). This notation reads "f of x" and means the function evaluated at x.
[Image] [Image]
Other methods for evaluating a function withthe graphing calculator are outlined above

Click on the LiveMath image to explore functions.

Note: Make sure you can generate a table on the calculator.
Use the Indep: Ask feature to set up the x values that you want.

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