In this lesson, you will investigate the relationship between the parameters $a$ and $b$ in the expression $a·b^x$ and a graph representing the function $f$ given by $f(x)=a·b^x$. You will start by identifying a function represented by a given graph and using the graph to make sense of a situation. You will also examine two abstract graphs, with unlabeled axes, and decide which one represents a given situation. In both cases, you will use your understanding of the connections between the parameters in an exponential expression and the features of an exponential graph to answer questions.

When you finish this lesson, you will be able to:

• Explain the meaning of the intersection of the graphs of two functions in terms of the situations they represent.
• Write an equation for the function given two points on a graph of an exponential function.

Here are the activities that will help you reach those goals:

• 5.13.1: Comparing Functions
• 5.13.2: Creating Exponential Functions from Graphs
  • 5.13.2: Self Check
  • 5.13.2: Additional Resources
• 5.13.3: Comparing Exponential Functions
  • 5.13.3: Self Check
  • 5.13.3: Additional Resources
• 5.13.4: Interpreting Features of an Exponential Graph

After that, you’ll practice and review.

• 5.13.5: Practice
• 5.13.6: Lesson Summary