Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 26

Topic

Exponential Functions

Description

This example showcases the graph of the exponential function y = -3 * e^x, where e is the mathematical constant approximately equal to 2.71828. The graph displays a decreasing curve with a y-intercept at ( 0 , -3 ). Students are tasked with graphing the y-intercept and determining if the function is decreasing or increasing.

Exponential functions with base e play a crucial role in various mathematical and scientific applications. By examining this example with a negative coefficient multiplying the entire function, students can develop a deeper understanding of how such modifications affect the behavior of natural exponential functions.

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 and bases, allowing students to observe how these elements interact to produce different graph characteristics. 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 twenty-sixth example. We have the natural exponential function multiplied by -3. How does this change the graph's behavior compared to our previous examples? Can you explain why the function is now decreasing instead of increasing, even though the exponent is still just x? As we continue exploring more functions with base e, try to predict how the sign and magnitude of the coefficient multiplying the function will affect the graph's appearance and behavior."

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