Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 18

Topic

Exponential Functions

Description

This example showcases the graph of the exponential function y = -3 * ( 2 )^4x. The graph displays a rapidly decreasing curve with a y-intercept at ( 0 , -3 ). Students are tasked with graphing the y-intercept and determining if the function is decreasing or increasing.

Exponential functions play a crucial role in various mathematical and real-world applications, from compound interest calculations to modeling population growth or decay. By examining diverse examples of exponential function graphs, students can develop a nuanced understanding of how different parameters influence the function's behavior.

Providing multiple worked-out examples is essential for students to fully grasp the concept of exponential functions. Each example presents a unique combination of coefficients, bases, and exponents, allowing students to observe how these elements interact to produce different graph characteristics. This approach helps students build intuition and analytical skills necessary for working with exponential functions in various contexts.

Teacher Script: "Now, let's look at our eighteenth example. We have a negative coefficient, a base greater than 1, and a larger exponent. How do these factors combine to create a rapidly decreasing function? Can you explain why the graph decreases more steeply than in our previous decreasing examples? As we continue exploring more functions, try to predict how the magnitude of the exponent will affect the steepness of the curve."

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