Math Example: Graphs of Logarithmic Functions: Example 05

Topic

Logarithmic Functions

Description

This example presents the graph of the logarithmic function y = log₁₀(4x + 2). The graph curves upward from the right side, demonstrating how the addition of a constant inside the logarithm affects the function's behavior. Students are asked to determine the domain of the function and identify whether it opens upward or downward.

Logarithmic functions are fundamental in mathematics and have wide-ranging applications in various fields, including physics, chemistry, and economics. This collection of examples helps teach logarithmic functions by showcasing different transformations and combinations of operations within the logarithmic equation. By examining these diverse examples, students can develop a deeper understanding of how changes in the equation impact the graph's appearance and properties.

Exploring multiple worked-out examples is essential for students to fully comprehend the nuances of logarithmic functions. Each example builds upon previous knowledge, introducing new concepts and transformations. This approach allows students to recognize patterns, make connections between different forms of logarithmic equations, and develop problem-solving skills that can be applied to more complex scenarios. By working through a variety of examples, students can build a robust understanding of logarithmic functions and their behavior.

Teacher's Script: Let's examine our fifth example, y = log₁₀(4x + 2). How does this graph compare to the basic logarithmic function we saw in the first example? Notice the shape is similar, but there's a change in position. Can you describe what's different? Think about how the addition of 2 inside the logarithm affects where the graph intersects the y-axis. How does this impact the domain of the function? Is it still x > 0, or has it changed? Use this information to determine if the graph opens upward or downward.

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