For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. g(3/2)

Key Concepts

Exponential Functions

Exponential functions are mathematical expressions in the form f(x) = a^x, where 'a' is a constant base and 'x' is the exponent. These functions exhibit rapid growth or decay depending on whether the base is greater than or less than one. Understanding the behavior of exponential functions is crucial for evaluating expressions like f(x) = 3^x and g(x) = (1/4)^x.

Evaluating Functions

Evaluating functions involves substituting a specific value for the variable in the function's expression. For example, to find g(3/2), you replace 'x' in g(x) = (1/4)^x with 3/2, resulting in g(3/2) = (1/4)^(3/2). This process is essential for calculating specific outputs of functions based on given inputs.

Rounding Numbers

Rounding numbers is the process of adjusting a numerical value to a specified degree of precision, often to make it easier to read or use. In this context, rounding to the nearest thousandth means adjusting the result of g(3/2) to three decimal places. This concept is important for presenting final answers in a clear and standardized format.