Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 3

Topic

Exponential Functions

Description

This example showcases the graph of the exponential function y = ( 0.9 )^-2x. Interestingly, despite the base being less than 1, the graph shows an increasing curve with a y-intercept at ( 0 , 1 ). Students are instructed to graph the y-intercept and determine if the function is decreasing or increasing.

Exponential functions play a crucial role in various mathematical and real-world applications, from compound interest calculations to modeling population growth or decay. By examining diverse examples of exponential function graphs, students can develop a nuanced understanding of how different parameters influence the function's behavior.

Providing multiple worked-out examples is essential for students to fully grasp the concept of exponential functions. Each example presents a unique combination of base and exponent, allowing students to observe how these elements interact to produce different graph shapes. This approach helps students build intuition and analytical skills necessary for working with exponential functions in various contexts.

Teacher Script: "Now, let's look at our third example. Notice something interesting here – even though our base is less than 1, the function is increasing! Can you figure out why? Think about the negative sign in front of the 2x in the exponent. How does this change the behavior of the function? As we continue exploring more examples, try to predict the graph's behavior based on the base and the sign of the exponent."

For a complete collection of math examples related to Graphs of Exponential Functions click on this link: Math Examples: Graphs of Exponential Functions Collection.