Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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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.
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Evaluating Composed Functions
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.
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