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Algebra >> Exponential and Logarithmic Functions >> Graphs of Exponential and Logarithmic Functions

Math Example: Graphs of Logarithmic Functions: Example 18

Math Example: Graphs of Logarithmic Functions: Example 18

Graph of y = -ln(15x)

Topic

Logarithmic Functions

Description

This example presents the graph of the negative natural logarithmic function y = -ln(15x). The graph opens downward, curving from right to left, demonstrating how the negative sign and multiplication inside the logarithm affect the function's behavior. The domain of this function remains x > 0, as the expression inside the natural logarithm must be positive.

Natural logarithmic functions, including their negatives and transformations, 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 natural logarithms, allowing students to 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 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 eighteenth example, y = -ln(15x). Compare this graph to the previous natural logarithm function. What are the main differences you notice? That's right, it's flipped upside down and shifted horizontally. Why do you think this happened? Consider the effect of the negative sign in front of ln(15x) and the multiplication by 15 inside the logarithm. How do these changes affect the range and y-intercept of the function? Is the domain different from the previous example? Why or why not?

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

Common Core Standards CCSS.MATH.CONTENT.HSF.IF.C.7, CCSS.MATH.CONTENT.HSF.IF.C.8.B, CCSS.MATH.CONTENT.HSF.BF.B.5, CCSS.MATH.CONTENT.HSF.IF.C.7.E, CCSS.Math.CONTENT.HSF.LE.A.2, CCSS.MATH.CONTENT.HSF.LE.A.3, CCSS.MATH.CONTENT.HSF.LE.A.4, CCSS.MATH.CONTENT.HSF.LE.B.5
Grade Range 9 - 12
Curriculum Nodes Algebra
    • Exponential and Logarithmic Functions
        • Graphs of Exponential and Logarithmic Functions
Copyright Year 2013
Keywords logarithmic functions, graphs