How many times have you heard your grandmother
say, “Your mother (father) did this very thing when they were a
teenager. You are so like her (him)”? Do you have your father's
nose or your mother's eyes? Just as you resemble your parents, math functions
resemble their parent (or basic) function. You have studied four types
of functions so far in Algebra I: linear, quadratic, exponential and power.
This lesson is a review of those functions and will allow you to identify
parent functions, describe the behavior of the child (function) based
upon certain attributes (coefficients) and graph the math function, all
in a matter of seconds! Your challenge is to determine similarities among
the coefficient effects between the four function types.
You have already learned about four types of functions: linear, quadratic, exponential and power. In this webquest you will determine if any similiarities exists amongst the functions as you manipulate the coefficients. You will present your results in a PowerPoint slideshow which will be graded according to the rubric presented in the Evaluation Section.
You 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 you need further practice on any of these topics, go to the Additional Resources Section on the XXXXXXXXXXXXXXXX section and follow the directions.
In algebra-speak you are going to predict the effect of transformations on parent functions, write the new equations and plot the new child function, and determine similarities between the coefficient effects on the four function families.
To accomplish this task you need some scratch paper, copies of the worksheets listed in the Process portion, a TI-83 graphing calculator and a pencil.
a. Effects of changing b in linear functions
c. Effects of changing X in exponential functions
d. Effects of changing X in power functions.