Math Example--Exponential Concepts--Graphs of Exponential Functions: Example 35

Topic

Exponential Functions

Description

This example illustrates the graph of the exponential function y = 2 * 10^x. The graph shows an increasing 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 fundamental in various scientific and engineering applications. By examining this example with a coefficient multiplying the entire function, 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 thirty-fifth example, we have the base-10 exponential function multiplied by 2. How does this change the graph's behavior compared to y = 10^x? Can you explain why the y-intercept is now at (0, 2) instead of (0, 1)? As we continue with more examples, try to predict how different coefficients multiplying the function will affect the graph's position and shape for base-10 functions."

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