This optional lesson provides additional practice investigating the relationship between the parameters and in the expression and a graph representing the function given by . Students start by identifying a function represented by a given graph and using the graph to make sense of a situation. They also examine two abstract graphs, with unlabeled axes, and decide which one represents a given situation. This level of abstraction is appropriate at this stage. It gives students an opportunity to apply what they have learned about the relationship between an exponential context and its graph, and to use graphs to better interpret the contexts. In both cases, they rely on their understanding of the connections between the parameters in an exponential expression and the features of an exponential graph (MP7) to answer questions.
Learning Goals
Identify the initial value and growth factor of an exponential function given a graph showing two points with non-consecutive input values.
Interpret the intersection of the graphs of two functions that represent a situation.
Student-Facing Goal
Let’s investigate what we can learn from graphs that represent exponential functions.
Student-Facing Targets
I can explain the meaning of the intersection of the graphs of two functions in terms of the situations they represent.
When I know two points on a graph of an exponential function, I can write an equation for the function.
Devices that can run Desmos (recommended) or other graphing technology should be available as an optional tool for students to select.
Activity 3
Devices that can run Desmos (recommended) or other graphing technology should be available as an optional tool for students to select.
Glossary
None
Standards Alignment
Building On
Addressing
HSF-IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
