Here are the essential concepts you must grasp in order to answer the question correctly.
Logarithmic Functions
Logarithmic functions, such as ƒ(x) = log₁₀ x, are the inverses of exponential functions. They express the power to which a base must be raised to obtain a given number. In this case, log₁₀ x asks what exponent you need to raise 10 to in order to get x. Understanding the properties of logarithms, including their domain and range, is essential for graphing them accurately.
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Graphing Techniques
Graphing techniques involve plotting points on a coordinate plane to visualize the behavior of a function. For logarithmic functions, key points include (1, 0) since log₁₀(1) = 0, and (10, 1) since log₁₀(10) = 1. Additionally, recognizing the asymptotic behavior as x approaches 0 (the graph approaches negative infinity) is crucial for accurately representing the function.
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Domain and Range
The domain and range of a function define the set of possible input values (domain) and the resulting output values (range). For the function ƒ(x) = log₁₀ x, the domain is x > 0, as logarithms are undefined for non-positive values. The range is all real numbers, indicating that the output can take any value from negative to positive infinity, which is important for understanding the graph's extent.
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