Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 8

Topic

Exponential Functions

Description

This example showcases the graph of the exponential function y = -4 * ( 0.25 )^3x. Interestingly, despite the negative coefficient, the graph shows an increasing curve with a y-intercept at ( 0 , -4 ). Students are tasked with determining 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 characteristics. This approach helps students build intuition and analytical skills necessary for working with exponential functions in various contexts.

Teacher Script: "Now, let's examine our eighth example. Notice something interesting here – even though we have a negative coefficient, the function is increasing! Can you figure out why? Think about the base being less than 1 and how it's raised to the power of 3x. How does this combination of factors affect the graph's behavior? As we continue exploring more examples, try to predict how different combinations of coefficients, bases, and exponents will influence 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.