Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 7

Topic

Exponential Functions

Description

This example showcases the graph of the exponential function y = 4 * ( 1/3 )^2x. The graph displays a decreasing curve with a y-intercept at ( 0 , 4 ). Students are instructed to 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 coefficients, bases, and exponents, 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 seventh example. We have a coefficient of 4, a fractional base, and an exponent of 2x. How do these elements combine to affect the graph's shape? Can you explain why the function decreases despite starting at a higher y-intercept? As we continue exploring more examples, try to predict the graph's behavior based on the coefficient, base, and exponent. How would changing each of these components alter the graph?"

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