Do you look like you mother or your father? Are your eyes or your
smile similar to someone in your family? But most important of all,
is your behavior like your Mom's or Dad's? Does your Mom ever say,
"You are just like your father!"? Math functions, like people, resemble
their parent functions. Even more important, if we know the behavior of
the parent we can predict the behavior of the "child". This unit
will allow you to identify the parent function, describe the behavior of
the child, and graph the function at a glance. You will be able to
impress friends and entertain at parties with your new-found mathematical
ability. So get started and "More Power to You"!
y = x
y = x2
y = 2x
y = x3
The Tasks:
After you finish this WebQuest you will be able to do the following:
locate points on the coordinate plane,
identify, graph, and write the equations for:
linear functions and their transformations,
quadratic functions and their transformations,
exponential functions and their transformations,
power functions and their transformations, and
apply the things that you learned to real life situations.
y = x
y = x2
y = 2x
y = x3
The Process:
This WebQuest will allow you to complete the tasks above and gain valuable
knowledge into the behavior of functions. To complete the tasks,
click on the indicated web sites and follow each set of directions.
You will find information that will "transform" your understanding of functions.
If at anytime you need a graphing calculator, visit EZGraph.
1. Ordered pairs are pairs of real numbers that describe
a point in The
Coordinate Plane. You will discover how to locate and name ordered
pairs. After you are confident that you understand the coordinate
plane, challenge your graph skills by visiting What's
the Point?. Also, for fun try the Colored
Grid.
2. What are functions? Relations
and Functions helps you investigate functions, relations, domain,
and range. It also helps you become familiar with function
notation which prepares you to begin your quest of function families. Algebra
Graphs gives you a preview of what to expect when you encounter head
of family equations.
3. Four
Basic Function Families outlines linear, quadratic, exponential, and
power functions. You will make tables of values and graph functions.
Here you can investigate the basic characteristics of the graphs of these
functions. The purpose of this section is to ensure that you understand
the general form and the basic behavior of these functions.
4. Be transformed with Fun
with Function Families. Head of family equations will be identified
and transformations will take place. For extra practice with
linear functions, Equations
of a Straight Line will do the trick. In graphing or analyzing
quadratic functions , it is important to find key elements. Parabola will
guide you to the discovery of the elements and increase your functional
vocabulary. EZGraph.
5. For real life applications, investigate populations changes
in a Trout
Pond. You will discover possible population growth patterns as
you make conjectures about what will happen next. Transformations
of Linear and Exponential Functions, also will give more practice on
horizontal shifts. While you are there, see if you can discover what a
flat tax is and how it might relate to straight lines.
y = x
y = x2
y = 2x
y = x3
The Evaluation:
You will be graded on your individual performance as described in the
diagram below. The diagram corresponds to the tasks listed earlier
in the WebQuest.
Beginning
1
Developing
2
Accomplished
3
Exemplary
4
Score
Locate
Points on the Coordinate Plane
Name the x and y axis.
Name the quadrants.
Locate a point in the first quadrant.
Locate points in each quadrant and on both axis.
Identify linear functions.
Recognize linear parent graph and equation.
Identify a reflection of a parent linear
function.
Identify a vertical compression or stretch of
a linear parent function.
Identify a right and left translation of a linear
parent function.
Identify quadratic functions.
Recognize parent quadratic graph and equation.
Identify a reflection of a parent quadratic function.
Identify a vertical compression or stretch of
a quadratic parent function.
Identify a right and left translation of a quadratic
parent function.
Identify exponential functions.
Recognize parent exponential graph and equation.
Identify a reflection of a parent exponential
function.
Identify a vertical compression or stretch of
a exponential parent function.
Identify a right and left translation of an exponential
parent function.
Identify power functions.
Recognize parent power graph and equation.
Identify a reflection of a parent power function.
Identify a vertical compression or stretch of
a power parent function.
Identify a right and left translation of a power
parent function.
y = x
y = x2
y = 2x
y = x3
Conclusion:
After completing this WebQuest, you will be able to identify the basic
four "head of family" equations and their graphs. In addition, you
will also be able to identify reflections, compressions, stretches, and
translations of these basic functions. This new found ability will greatly
enhance your Algebra skills. For a challenge, try Logistic
Growth. Good luck in future quests and "More Power to You"!
y = x
y = x2
y = 2x
y = x3
Credits & References:
I would like to thank Edith Lancaster and Jo Ann Simmons for writing
a wonderful unit on function families. I had begun to write my own when
I discovered their work. I would also like to thank Stan Holland
for saving my life when my disk malfunctioned and Dr. Bruce Lewis for helping
so much with my divider bars. I would also like to thank Zona
Land for the picture and the background.
y = x
y = x2
y = 2x
y = x3
Teacher Advice:
This lesson is suitable for 8th-9th graders who are taking Algebra I.
In some instances seventh graders can also benefit from this WebQuest.
Critical thinking skills are very much a part of this WebQuest.
Critical thinking consists of three components: evaluating, analyzing,
and connecting. The attributes included in my WebQuest in the evaluating
part of critical thinking are assessing information for its reliability
and usefulness, prioritizing a set of options according to their importance,
and verifying arguments and hypotheses through reality testing. The
analyzing components of critical thinking which are included in my WebQuest
are recognizing patterns, classifying objects into categories, and identifying
main or central ideas. The connecting components of critical thinking
included in my WebQuest are comparing and contrasting similarities and
differences, logical thinking, and identifying causal relationships between
events or objects and predicting possible effects.
The learners will need to have a working knowledge of a graphing
calculator. They will also need to know how to solve for one variable in
terms of another one.
The lesson will take approximately three to four days on a fifty-five
minute period schedule. The lesson begins with the coordinate plane and
progresses to functions, domain, range, and function notation. Then
reflections, translations, compressions, and stretches are covered after
students can readily identify the parent functions.
The teacher needs to know how to use a graphing calculator.
The WebQuest also requires that the teacher be comfortable with reflections,
translations, compressions, and stretches of functions.
The lesson can be used totally as a class assignment with the students
working in groups or individually. A very good unit to use for this
is Fun with Function Families by Edith Lancaster and Jo Ann Simmons. They
teach a fun approach to the graphs called "Mathercise" where the students
physically make the graphs with their arms. On test day you will
realize how well this works when you see students trying to move their
arms without being noticeable.
One teacher is enough to implement this lesson, however, a class
set of graphing calculators is a necessity.
