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Hyperglossary
Assignment
Section 4 - 7
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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
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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.
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.
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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