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. ƒ(-5/2)

Key Concepts

Exponential Functions

Exponential functions are mathematical expressions in the form f(x) = a^x, where 'a' is a positive constant and 'x' is the variable. These functions exhibit rapid growth or decay depending on the base 'a'. In this question, f(x) = 3^x represents exponential growth, while g(x) = (1/4)^x represents exponential decay.

Evaluating Functions

Evaluating a function involves substituting a specific value for the variable in the function's expression. For example, to find f(-5/2) for the function f(x) = 3^x, you replace 'x' with -5/2, resulting in f(-5/2) = 3^(-5/2). This process is essential for determining the output of the function at a given input.

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 the function evaluation to three decimal places. This is important for presenting answers clearly and accurately in mathematical contexts.