Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 14

Topic

Exponential Functions

Description

This example presents the graph of the exponential function y = 2^0.25x. The graph displays an increasing curve with a y-intercept at ( 0 , 1 ). 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 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 fourteenth example. We're back to an increasing function, but notice how the curve is less steep than in Examples 11 and 12. Can you explain why this happens when the exponent is a fraction between 0 and 1? As we continue exploring more functions, try to predict how different exponents will influence the graph's rate of increase or decrease."

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