Math Example--Exponential Concepts--Exponential Functions in Tabular and Graph Form: Example 4

Topic

Exponential Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the exponential function y = 3 * 2^2x. The image provides a visual representation of the function, showing both a table of coordinates and a graph plotted on a coordinate plane. The table lists x-y coordinates for x values ranging from -2 to 2, with corresponding y values calculated using the given function.

Exponential functions are a crucial topic in mathematics, particularly in algebra and calculus. They model various real-world phenomena, such as population growth, compound interest, and radioactive decay. This collection of examples helps teach the topic by providing students with multiple representations of exponential functions, allowing them to see the relationship between the equation, table of values, and graphical representation.

Seeing multiple worked-out examples is essential for students to fully grasp the concept of exponential functions. Each example in this collection showcases a different variation of the exponential function, helping students understand how changes in the base, coefficient, and exponent affect the shape and behavior of the graph. This approach reinforces the concept through repetition and variation, allowing students to develop a deeper understanding of the underlying principles.

Teacher Script: "Let's examine this exponential function together. Notice how the table shows us the x and y values, and how they correspond to points on the graph. Can you see how the y values grow rapidly as x increases? This is a key characteristic of exponential growth. Try to predict what the next point would be if we extended the table to x = 3. How does this graph compare to a linear function you've seen before?"

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