In this lesson, students study exponential functions and their graphs in context. Given a graph or a description of a relationship, they write one quantity as a function of another and then use the function to answer questions about the context. They also produce graphs of exponential functions, paying close attention to the appropriate domain and range, which are both restricted by the context (MP2 and MP6).
- Determine whether a graph that represents a situation should be continuous or discrete.
- Interpret graphs of exponential functions and equations written in function notation to answer questions about a context.
- Use function notation to describe an exponential relationship represented by a graph.
- Use graphing technology to graph exponential functions and analyze their domains.
Let’s find some meaningful ways to represent exponential functions.
The blank paper is for the Paper Folding activity. Consider one sheet per student, or to save paper, one sheet for every 2 students.
For the info gap activity, prepare one set of cut-up slips for every 2 students.
Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)
- I can analyze a situation and determine whether it makes sense to connect the points on the graph that represents the situation.
- When I see a graph of an exponential function, I can make sense of and describe the relationship using function notation.
An exponential function is a function that has a constant growth factor. Another way to say this is that it grows by equal factors over equal intervals. For example, \(f(x)=2 \boldcdot 3^x\) defines an exponential function. Any time \(x\) increases by 1, \(f(x)\) increases by a factor of 3.