Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 20

Topic

Exponential Functions

Description

This example presents the graph of the exponential function y = -6 * ( 2 )^0.75x. The graph displays a decreasing curve with a y-intercept at ( 0 , -6 ). Students are asked to graph the y-intercept and determine whether the function is decreasing or increasing.

Exponential functions are a fundamental concept in mathematics, with applications ranging from financial modeling to scientific research. By studying various examples of exponential function graphs, students can develop a deeper understanding of how different parameters affect the function's behavior and shape.

Providing students with multiple worked-out examples is crucial for mastering the concept of exponential functions. Each example introduces 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 diverse contexts.

Teacher Script: "Let's examine our twentieth example. We have a negative coefficient, a base greater than 1, and an exponent between 0 and 1. How do these elements combine to affect the graph's shape? Can you explain why the function is decreasing despite having a base greater than 1? As we continue exploring more functions, try to predict how the interplay between negative coefficients and fractional exponents will influence the graph's behavior."

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