Math Example: Graphs of Logarithmic Functions: Example 04

Topic

Logarithmic Functions

Description

This example showcases the graph of the logarithmic function y = -log₁₀(5x). The graph is a reflection over the x-axis compared to log functions without a negative sign, and it's also horizontally compressed due to the factor of 5 inside the logarithm. Students are tasked with determining the domain and direction of this graph.

Logarithmic functions are essential in various fields, including science, engineering, and finance. They are particularly useful for modeling phenomena that exhibit exponential growth or decay. This collection of examples helps teach logarithmic functions by presenting a variety of equations with different transformations, allowing students to visualize and understand how these changes affect the graph's shape, position, and behavior.

Providing multiple worked-out examples is crucial for students to fully grasp the concept of logarithmic functions. Each example builds upon previous ones, introducing new transformations and combinations of operations. This approach helps students recognize patterns, understand the effects of different parameters, and develop the ability to predict how changes in the equation will impact the graph. By working through diverse examples, students can build a robust understanding of logarithmic functions and their properties.

Teacher's Script: Now, let's examine our fourth example, y = -log₁₀(5x). Take a moment to compare this graph to the previous examples we've seen. What similarities and differences do you notice? How does the negative sign affect the graph compared to example 3? What about the factor of 5 inside the logarithm - how does that change the graph's appearance? Consider how these transformations impact the domain and range of the function.

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