Graphing Logarithmic Functions with Transformations

Learning Context

Purpose

Rational:

The ability to translate a given equation into an image expedites the process of finding a solution to a given problem. Moreover, when learners see a graphic image and receive some key facts about the graph, with an understanding of transformations, one is able to derive the equation for the image. This process of translation and transformation is a necessity in the informational age. Overall, graphs allow a learner to solve mathematical equations, physical problems, as well as make logical inferences with an image. Lastly, graphing is an essential part on the New York State Algebra II and Trigonometry Regents Exam, to prevent disservice to the learner as well as to insure proper preparation for the exam graphing with transformations ought to be addressed.

Enduring Understanding

Enduring Understanding:

Graphing with transformations can generate images on a host of parent functions.
Graphs allow data to be represented visually and opportunities to find and compare trends, to make logical inferences.

Essential Questions

Essential Question:

What will happen to the graphs y=f(x) of when a constant k is introduced?

Guiding Questions:

What are the characteristics the parent function?
How does one read a graph?
Where does the constant k translate the image?
When is it appropriate to use transformations?

Overview of What Students Need to Know

There are no students with special needs and therefore no need for modifications environment, or instruction type. Moreover, this Learning Experience is developed with modifications in place which, are specifically identified, rationalized, and supported in the Modification, to insure every learner is successful.

Prior to Implementation:

The effects on a familiar graph of f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative);and how the given values of k effect the graphs.
How to identify the parent function given y=f(x).
How to graph a function y=f(x) given using a table of values.

During Implementation:

The characteristics of the logarithmic function y=f(x)= log_b(x)
How to construct a table of values.
How to graph a function.

After Implementation:

The effects on y=f(x)= log_b(x) when replacing f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative).
How to construct a transformations table of values.
How to graph the function y=f(x)= log_b(x) after all transformations have been completed.

Classroom Rules

This learning experience is designed to address two class periods of Algebra II and Trigonometry honors students, of mixed grade levels (tenth and eleventh) at Saint Joseph's Collegiate Institute, in Buffalo New York. The three sections of students, totaling sixty-five learners, share the same set of classroom rules.