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 of f(x) = a^x, where 'a' is a positive constant. In this case, g(x) = (3/2)^x represents an exponential function with a base greater than 1, indicating that the function will grow as x increases. Understanding the behavior of exponential functions is crucial for graphing them accurately.
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Table of Coordinates
Creating a table of coordinates involves selecting various x-values and calculating the corresponding g(x) values. This process helps in plotting points on a graph, providing a visual representation of the function's behavior. For g(x) = (3/2)^x, choosing a range of x-values, including negative, zero, and positive values, will illustrate how the function behaves across different intervals.
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Graphing Utilities
Graphing utilities are software tools or calculators that allow users to visualize mathematical functions. They can confirm the accuracy of hand-drawn graphs by providing a precise graphical representation of the function. Using a graphing utility for g(x) = (3/2)^x can help students verify their plotted points and understand the overall shape and characteristics of the exponential curve.
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