The student should have already learned about four types of functions: linear, quadratic, exponential and power. In this webquest, the student will determine if any similiarities exist amongst the functions as they manipulate the coefficients. Students will present their results in a PowerPoint slideshow which will be graded according to the rubric presented in the Evaluation section.
Students should already be able to
*identify the coefficients in a given function including the zero coefficient,
*identify a function and state its domain and range,and
*identify the general form and basic behavior of four different parent functions.
If students need further practice on any of these topics, go to the Resources Section and follow the directions.
In algebra-speak students are going to predict the effect of transformations on parent functions, write the new equations and plot the new child function, and determine if any similarities exist between the coefficient effects on the four function families.
To accomplish this task students need some scratch paper, copies of the worksheets listed in the Process portion, a TI-83 graphing calculator or emulator and a pencil.
Students are expected to be able to use the function plotter software FG Function Grapher - 2D proficiently. They also must be proficient in using a TI-83 calculator or emulator. They also must be able to recogize the the parent functions both graphically and in function form. The should be able to identify the range and domain for any given function no matter what form it is presented in (equation, graph, table of values).
Texas Mathematical Standards addressed are:
A.b.4.A the student finds specific function values, simplifies polynomial expressions, transforms and solves equations, and factors as necessary in problem situations
A.c.1.C the student translates among and uses algebraic, tabular, graphical, or verbal descriptions of linear functions
A.c.2.C the student investigates, describes, and predicts the effects of changes in m and b on the graph of y=mx+b
A.d.1.C the student investigates, describes, and predicts the effects of changes in c on the grpah of y=x^2+c
NCTM standards addressed are:
Download and print the following:
a. Effects of changing b in linear functions
b. Effects of changing c in quadratic functions
c. Effects of changing X in exponential functions
d. Effects of changing X in power functions.
Describe briefly how the lesson is organized. Does it involve more than one class? Is it all taught in one period per day, or is it part of several periods? How many days or weeks will it take? Is it single disciplinary, interdisciplinary, multidisciplinary or what?
If students are divided into groups, provide guidelines on how you might do that.
If there are misconceptions or stumbling blocks that you anticipate, describe them here and suggest ways to get around them.
What skills does a teacher need in order to pull this lesson off? Is it easy enough for a novice teacher? Does it require some experience with directing debates or role plays, for example?
If you can think
of ways to vary the way the lesson might be carried out in different situations
(lab vs. in-class, for example), describe them here.