Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 10

Topic

Exponential Functions

Description

This example illustrates the graph of the exponential function y = -5 * ( 0.5 )^0.75x. The graph shows an increasing curve with a y-intercept at ( 0 , -5 ), despite the negative coefficient. Students are asked to graph the y-intercept and determine if the function is decreasing or increasing.

Exponential functions are a crucial topic in mathematics, with applications in various fields such as physics, biology, and economics. By examining multiple examples of exponential function graphs, students can develop a deeper understanding of how different parameters affect the shape and behavior of these functions.

Providing students with a variety of worked-out examples is essential for building a comprehensive understanding of exponential functions. Each example highlights different aspects of these functions, allowing students to recognize patterns and make connections between different representations. This approach helps reinforce key concepts and improves students' ability to analyze and interpret exponential functions in various contexts.

Teacher Script: "In this tenth example, we have an interesting variation. Notice that we have a negative coefficient, a base less than 1, and an exponent less than 1. How do these factors combine to create an increasing function? Can you explain why the graph starts at a negative y-intercept but still increases? As we continue with more examples, try to predict how changes in the coefficient, base, and exponent 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.