In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. g(x) = (3/2)^x

Key Concepts

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.

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.

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.