Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 19

Topic

Exponential Functions

Description

This example illustrates the graph of the exponential function y = 5 * ( 2 )^0.5x. The graph shows an increasing curve with a y-intercept at ( 0 , 5 ). 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 nineteenth example, we have a positive coefficient, a base greater than 1, but an exponent less than 1. How does this combination affect the graph's behavior? Can you explain why the function increases more slowly than some of our previous increasing examples? As we continue with more examples, try to predict how fractional exponents will influence the graph's rate of increase."

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