Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 9

Topic

Exponential Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the exponential function y = -0.5 * 2^x. The image presents both a table of values and a graph, displaying the function's behavior. The table lists x-y coordinates for x values from -2 to 2, with corresponding y values calculated using the given function. This representation helps students visualize an exponential function with a negative fractional coefficient.

Exponential functions are a fundamental concept in mathematics, with applications in various fields such as finance, physics, and biology. This collection of examples serves to teach the topic by providing students with diverse representations of exponential functions. By examining different variations of these functions, students can develop a comprehensive understanding of how changes in the equation affect the resulting graph and table of values.

The importance of multiple worked-out examples in mathematics education cannot be overstated. Each example in this series offers a unique perspective on exponential functions, allowing students to recognize patterns and make connections between different representations. This approach helps reinforce key concepts and promotes a deeper understanding of the subject matter, ultimately leading to improved problem-solving skills and mathematical fluency.

Teacher Script: "As we look at this example, pay attention to how the negative fractional coefficient -0.5 affects the graph. Notice how the function decreases as x increases, unlike the growth we saw in some previous examples. Can you describe how this graph differs from the ones with integer coefficients? What do you think would happen if we changed the coefficient to -0.25 or -0.75? How would this impact the y-intercept and the rate of decrease?"

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