Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 2

Topic

Exponential Functions

Description

This example presents the exponential function y = 4 * 2^x through a table of x-y coordinates and its corresponding graph. The table shows five key points: (-2, 1), (-1, 2), (0, 4), (1, 8), and (2, 16). These points are then plotted on a graph, demonstrating how the function grows exponentially as x increases.

Exponential functions are fundamental in mathematics, with applications ranging from finance to physics. This collection of examples aids in teaching the topic by showcasing various forms of exponential functions, allowing students to observe how changes in coefficients and bases affect the function's behavior and graph shape.

Exposure to multiple worked-out examples is crucial for students to develop a comprehensive understanding of exponential functions. Each example builds upon the previous one, helping students identify patterns and develop intuition about exponential growth. This approach enables learners to construct a solid foundation for tackling more advanced problems involving exponential functions.

Teacher Script: "Compare this graph to the previous example. How does the coefficient 4 affect the y-intercept and the overall shape of the graph? Notice that while the base is still 2, the y-values are now four times larger than in the previous example for each x-value. This illustrates how the coefficient impacts the function's behavior while maintaining the same exponential growth rate."

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