Question

Graph each function. $$f(x)=\log _{10} x$$

   Graph each function.
$$f(x)=\log _{10} x$$

A Graphical Approach to College Algebra

A Graphical Approach to College Algebra

John… 6th Edition

Chapter 5, Problem 40

Instant Answer

Solved by Expert Ankit Gupta

07/17/2020

Step 1

The graph of the function $f(x) = \log_{10} x$ is a curve that increases as x increases, but at a decreasing rate. The graph passes through the point (1,0) because any number raised to the power of 0 is 1. Show more…

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Graph each function. $$f(x)=\log _{10} x$$

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Key Concepts

Logarithmic Functions

Logarithmic functions are the inverses of exponential functions. They return the exponent that a given base must be raised to in order to yield a specific value. Understanding their nature helps in analyzing their unique growth patterns and transformation properties.

Domain and Range of Logarithmic Functions

The domain of any logarithmic function consists only of positive real numbers, as the logarithm is undefined for zero and negative numbers. Its range, however, includes all real numbers, meaning the output of a logarithmic function can be any real number.

Vertical Asymptote

A key feature of logarithmic functions is the vertical asymptote, typically found along the y-axis (e.g., x = 0). As the input values approach zero from the positive side, the function values decrease without bound, approaching negative infinity.

Inverse Relationship to Exponential Functions

Since logarithmic functions are the inverses of exponential functions, their graphs can be obtained by reflecting the graph of the corresponding exponential function over the line y = x. This relationship is crucial for understanding and sketching the behavior of logarithmic graphs.

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