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

Math Example: Graphs of Logarithmic Functions: Example 07

Math Example: Graphs of Logarithmic Functions: Example 07

Graph of y = log_10(4x) + 2

Topic

Logarithmic Functions

Description

This example illustrates the graph of the logarithmic function y = log10(4x) + 2. The graph curves upward, starting from the right, demonstrating how the addition 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 play a crucial role in various mathematical and scientific applications, from modeling exponential growth and decay to solving complex equations. This collection of examples helps teach logarithmic functions by presenting a range of equations with different parameters and transformations, allowing students to visualize and understand how these changes impact the graph's shape, position, and properties.

Exploring multiple worked-out examples is vital for students to develop a comprehensive understanding of logarithmic functions. Each example builds upon previous knowledge, introducing new concepts and transformations. This approach helps students recognize patterns, make connections between different forms of logarithmic equations, and develop problem-solving skills that can be applied to more complex scenarios.

Teacher's Script: Let's examine our seventh example, y = log10(4x) + 2. How does this graph compare to the basic logarithmic function we saw earlier? Notice the shape is similar, but there are changes in both vertical and horizontal positions. The multiplication by 4 inside the logarithm affects the graph's horizontal position, while the addition of 2 outside the logarithm impacts the vertical position. These transformations don't change the domain, which remains x > 0, but they do shift the y-intercept. Can you identify where the graph now intersects the y-axis?

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