Math Example: Graphs of Logarithmic Functions: Example 08

Topic

Logarithmic Functions

Description

This example showcases the graph of the logarithmic function y = log₁₀(5x) - 3. The graph curves upward from the right side, demonstrating how the subtraction of a constant outside the logarithm and multiplication inside the logarithm affect the function's behavior. The domain of this function is x > 0, as the logarithm is only defined for positive values inside the parentheses.

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.

Teacher's Script: Now, let's examine our eighth example, y = log₁₀(5x) - 3. Compare this graph to the previous examples we've seen. How does the multiplication by 5 inside the logarithm affect the graph's horizontal position? What about the subtraction of 3 outside the logarithm - how does that change the graph's vertical position? Notice that despite these transformations, the domain remains x > 0. Can you predict where this graph will intersect the y-axis? Remember, logarithmic functions always have a vertical asymptote at x = 0.

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