Evaluating Exponential Functions Use a calculator to...

Evaluating Exponential Functions Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals.
$$
g(x)=\left(\frac{4}{3}\right)^{3 x} ; \quad g\left(-\frac{1}{2}\right), g(\sqrt{6}), g(-3), g\left(\frac{4}{3}\right)
$$

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Key Concepts

Exponential Functions

Exponential functions are mathematical expressions in which a constant base is raised to a variable exponent. They often model growth or decay processes and are characterized by their rapid increases or decreases as the exponent changes.

Properties of Exponents

The properties of exponents provide rules for simplifying expressions where exponents are involved, such as multiplying powers with the same base, raising a power to a power, or handling negative and fractional exponents. These rules are foundational for understanding and manipulating exponential functions.

Function Evaluation

Function evaluation involves substituting a given input value into a function and calculating the corresponding output. This process verifies that the function behaves as expected for various inputs, and it is particularly important when working with non-linear functions like exponentials.

Numerical Approximation and Rounding

Numerical approximation and rounding involve calculating the value of a function using a calculator and then adjusting the result to a specified degree of precision, such as three decimal places. This ensures consistency and clarity in presenting results, especially when dealing with irrational or otherwise non-terminating numbers.

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