Quiz and Graphing Exponential Functions
Lesson 4 of 11
Objective: SWBAT demonstrate that they can apply the properties of exponents and solve exponential equations that do not require logarithms; students will produce graphs of exponential equations.
To be successful on Quiz - Solving equations with logs.doc students must be able to rewrite exponential expressions, solve equations with logarithms, and evaluate logarithmic expressions. This quiz is completed without a calculator and is designed to assess students' ability to rewrite expressions in a purposeful way [MP2].
Work for Early Finishers
Because my students vary in how quickly they complete assessments, I make sure to provide something for the early finishers to do. This quiz includes everything we have learned thus far in the unit, so there is no material for my students to practice. When this is the case, I select one of the following as work for early finishers:
1. Some geometry review problems, like WS Geometry Review.doc
2. Some test prep problems, either for the SAT or our state assessment
3. An interesting article from a recent newspaper that is related to math/statistics.
Graphs of exponential functions have many variations and are more difficult for my students than any other graph we study. To give my students a sense of what these graphs look like, I start by animating a graph in Desmos. I discuss how to make Desmos animations in the reflection Desmos for Conceptual Understanding. While showing students this animation, I introduce special features of the graph, like the horizontal asymptote, the end behavior, and how the average rate of change in these functions changes at a constant rate [MP2, MP6].
Once my students have the big picture of how the parameters in the function y=a*b^x+k affect the graph, I walk them through a strategy for producing a graph of an exponential function when the values of a, b, and k are known.
I suggest to students that they first plot the horizontal asymptote, y=k. They should then focus on the values of a and b to determine the end behavior of the function. When the have determined whether the function approaches k on the left or the right and whether it goes towards infinity or negative infinity on the other side, they are ready to choose some points to plot and connect.
My students generally need a great deal of practice in this skill. I provide this practice and gather information about their progress by passing out individual graphing white boards and putting functions on the board. I ask students to hold up their work when they are done and then give each student a thumbs up or a thumbs down.
When we have practiced as a group and I am confident that my students are ready to work independently, I distribute WS graphing exponential functions.doc and tell my students that this homework assignment will be checked the following day.