Math Example: Graphs of Logarithmic Functions: Example 16

Topic

Logarithmic Functions

Description

This example presents the graph of the negative natural logarithmic function y = -ln(x). The graph opens downward, curving from right to left, demonstrating how the negative sign affects the behavior of the natural logarithm. The domain of this function remains x > 0, as the natural logarithm is only defined for positive real numbers.

Natural logarithmic functions, including their negatives, are essential in various fields such as calculus, physics, and engineering. They are particularly useful for modeling decay processes and inverse exponential relationships. This collection of examples helps teach logarithmic functions by presenting various transformations of both common and natural logarithms, allowing students to understand how these changes affect the graph's shape and position.

Providing multiple worked-out examples is crucial for students to fully grasp the concept of logarithmic functions and their transformations. Each example builds upon previous ones, introducing new variations and 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 of logarithmic functions.

Teacher's Script: Now, let's examine our sixteenth example, y = -ln(x). Compare this graph to the previous natural logarithm function. What's the main difference you notice? That's right, it's flipped upside down. Why do you think this happened? Consider the effect of the negative sign in front of ln(x). How does this change affect the range of the function? Is the domain different from the previous example? Why or why not? Can you identify where this function intersects the x-axis? How does this point relate to the intersection point in the previous example?

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