In Exercises 43– 48, match the function with its graph from choices A–F. ƒ(x) = log￬2 x

Key Concepts

Logarithmic Functions

Logarithmic functions, such as f(x) = log₂(x), are the inverses of exponential functions. They express the power to which a base must be raised to obtain a given number. Understanding the properties of logarithms, including their domain (x > 0) and range (all real numbers), is essential for analyzing their graphs.

Graphing Logarithmic Functions

The graph of a logarithmic function typically has a vertical asymptote at x = 0 and passes through the point (1, 0), since log₂(1) = 0. As x increases, the function rises slowly, reflecting the nature of logarithms growing without bound but at a decreasing rate. Familiarity with these characteristics aids in matching the function to its graph.

Transformations of Functions

Transformations of functions involve shifting, reflecting, stretching, or compressing the graph of a function. For logarithmic functions, horizontal shifts can occur when the input is adjusted (e.g., log₂(x - h)), while vertical shifts occur when a constant is added or subtracted from the function (e.g., log₂(x) + k). Recognizing these transformations is crucial for accurately interpreting and matching graphs.