Math Example: Graphs of Logarithmic Functions: Example 13

Topic

Logarithmic Functions

Description

This example illustrates the graph of the logarithmic function y = log₁₀(2x + 5) - 3. The graph opens upward, demonstrating how the combination of multiplication and addition inside the logarithm, along with subtraction outside the logarithm, affect the function's behavior. The domain of this function is x > -2.5, as the expression inside the logarithm must be positive.

Logarithmic functions play a crucial role in various mathematical and scientific applications, from modeling exponential growth and decay to solving complex equations. This collection of examples helps teach logarithmic functions by presenting a range of equations with different parameters and transformations, allowing students to visualize and understand how these changes impact the graph's shape, position, and properties.

Exploring multiple worked-out examples is vital for students to develop a comprehensive understanding of logarithmic functions. Each example builds upon previous knowledge, introducing new concepts and transformations. This approach helps students recognize patterns, make connections between different forms of logarithmic equations, and develop problem-solving skills that can be applied to more complex scenarios.

Teacher's Script: Let's examine our thirteenth example, y = log₁₀(2x + 5) - 3. How does this graph compare to the previous two examples? Notice that we have addition inside the logarithm like in example 11, but subtraction outside like in example 12. How do these combinations affect the graph's position? The domain is x > -2.5. Can you explain why? How does the subtraction of 3 outside the logarithm impact the graph's vertical position? Can you predict where this graph will intersect the y-axis?

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