Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 40

Topic

Exponential Functions

Description

This example illustrates the graph of the exponential function y = -2 * 10^0.75x. The graph shows a decreasing curve with a y-intercept at ( 0 , -2 ). Students are asked to graph the y-intercept and determine if the function is decreasing or increasing.

Exponential functions with base 10 are crucial in various scientific and engineering applications. By examining this example with a negative coefficient multiplying the function and a fractional coefficient in the exponent, students can develop a deeper understanding of how such modifications affect the behavior of base-10 exponential functions.

Providing students with a variety of worked-out examples is essential for building a comprehensive understanding of exponential functions. Each example highlights different aspects of these functions, allowing students to recognize patterns and make connections between different representations. This approach helps reinforce key concepts and improves students' ability to analyze and interpret exponential functions in various contexts.

Teacher Script: "In this fortieth example, we have the base-10 exponential function multiplied by -2, and 0.75x in the exponent. How do these changes affect the graph's behavior compared to our previous examples? Can you explain why the function is decreasing despite having a positive exponent? As we conclude our exploration of exponential functions, try to summarize how the combination of a negative coefficient outside the exponential and a fractional positive coefficient inside influences the graph's steepness and direction."

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