Lesson Plan: Exponential Functions
Course Information
Course: Mathematics
Class: 11
Duration: 40 min
Technological Equipment:A Smart board
Content
Exponential functions and their graphs
Learning Outcomes
Students can explain exponential functions.
- When a is a positive real number different than 1, students will be able to draw the graph of the functions f(x)= ax; when b and c are real numbers, students will be able to draw the graph of the function f(x)= ax+b + c
- Students will be able to show that f function is increasing for a > 1 and that f function is decreasing for 0 < a < 1.
- Students will be able to show that exponential functions are bijective functions.
- The concept of exponential functions will be covered and their graphs will be observed.
- A graph of an exponential function with a given formula will be drawn.
- First of all, students will be asked to discuss in pairs how they can draw the graph of the function f(x) =
for a = 2 and a = 1/2. They will be told that they can replace x with integer values of f that are easy to calculate. After this point, students will be asked to discuss what kind of features the f function will have and what its graph will be like if a=1 is chosen. Finally, students will be asked to discuss what kind of values the statement ax will take for both integer and non-integer real numbers of x when it is a=0 and a= -2. - Geogebra will be used for the visual support of the graphs on the interactive board.
- In this course, graphic visuals will be shown after students engage in discussions.
- Students do not need to have any additional knowledge for the technology supported Geogebra program to be used in the lesson. However, they are told that they will be provided help, if they need it, about how to install the program in their tablet PCs and how they will use it.
- Conducting the lesson based on technology supported materials might break the flow of the lesson especially in the shortage of the energy resources the technology in question depends on. For instance, in case of a power cut, a lesson plan based solely on an interactive board will be useless.
- Therefore, in the planning phase of a lesson, this point should be kept on mind.
- In this lesson plan, two kinds of Geogebra exercise will be used, but even without them, students will be able to visualize the concept through in-class discussions.
Questions
1. Draw the graph of the function , . 2. Draw the graph of the function , .