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(-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 case, 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(-2) for the function f(x) = 3^x, you replace 'x' with -2, resulting in f(-2) = 3^(-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 number to a specified degree of accuracy, often to make it simpler or more understandable. In this context, rounding to the nearest thousandth means keeping three decimal places. For instance, if the result of f(-2) is 0.1111, it would be rounded to 0.111.