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Pre-Lesson: See Extra Support Materials for Algebra 1, Unit 6, Lesson 13.
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.
Let’s investigate what we can learn from graphs that represent exponential functions.