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Math Example: Graphs of Logarithmic Functions: Example 06

Math Example: Graphs of Logarithmic Functions: Example 06

Graph of y = log_10(5x - 3)

Topic

Logarithmic Functions

Description

This example showcases the graph of the logarithmic function y = log10(5x - 3). The graph starts from the right and curves upwards, demonstrating how the subtraction of a constant inside the logarithm affects the function's behavior. Students are tasked with determining the domain of the function and identifying whether it opens upward or downward.

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 sixth example, y = log10(5x - 3). Take a moment to compare this graph to the previous examples we've seen. What similarities and differences do you notice? How does the subtraction of 3 inside the logarithm affect the graph's position? Consider how this transformation impacts 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. Can you predict what value of x would make the expression inside the logarithm equal to zero?

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