In Exercises 79–82, use a graphing utility and the change-of-base property to graph each function. y = log2 (x + 2)

Key Concepts

Logarithmic Functions

Logarithmic functions are the inverses of exponential functions and are defined as y = log_b(x) if and only if b^y = x, where b is the base. They are used to solve for the exponent in equations involving powers. Understanding the properties of logarithms, such as the product, quotient, and power rules, is essential for manipulating and graphing these functions.

Change-of-Base Formula

The change-of-base formula allows you to convert logarithms from one base to another, expressed as log_b(a) = log_k(a) / log_k(b) for any positive k. This is particularly useful when using calculators or graphing utilities that may only support certain bases, such as base 10 or base e. This formula helps in evaluating logarithmic expressions and graphing them accurately.

Graphing Utilities

Graphing utilities, such as graphing calculators or software, are tools that allow users to visualize mathematical functions. They can plot functions, including logarithmic ones, by calculating values over a specified range. Understanding how to input functions correctly and interpret the resulting graphs is crucial for analyzing the behavior of logarithmic functions, such as their domain, range, and asymptotic behavior.