Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 36

Topic

Exponential Functions

Description

This example presents the graph of the exponential function y = -3 * 10^x. The graph displays a decreasing curve with a y-intercept at ( 0 , -3 ). Students are asked to graph the y-intercept and determine whether 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, students can develop a deeper understanding of how such modifications affect the behavior of base-10 exponential functions.

Providing students with multiple worked-out examples is essential for mastering the concept of exponential functions. Each example introduces a unique combination of coefficients and bases, 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 thirty-sixth example. We have the base-10 exponential function multiplied by -3. How does this change the graph's behavior compared to y = 10^x? Can you explain why the function is now decreasing instead of increasing? As we continue exploring more functions with base 10, try to predict how the sign and magnitude of the coefficient multiplying the function will affect the graph's appearance and 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.