Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = (0.6)^x

Verified step by step guidance

1. Identify the function given: \(f(x) = (0.6)^x\). This is an exponential function where the base is 0.6, which is between 0 and 1, indicating exponential decay.
2. Choose a set of x-values to evaluate the function. Typically, select integer values around zero, such as \(x = -2, -1, 0, 1, 2\), to get a good range of points.
3. Calculate the corresponding y-values by substituting each chosen x-value into the function: \(f(x) = (0.6)^x\). For example, for \(x=1\), compute \(f(1) = (0.6)^1\); for \(x=-1\), compute \(f(-1) = (0.6)^{-1}\), and so on.
4. Create a table of coordinates with your x-values and their corresponding y-values. This table will help you plot points accurately on the graph.
5. Plot the points from your table on a coordinate plane and connect them smoothly to reflect the exponential decay shape. Optionally, use a graphing utility to confirm the accuracy of your hand-drawn graph.

Key Concepts

Exponential Functions

An exponential function has the form f(x) = a^x, where the base a is a positive constant. The function grows or decays depending on whether a is greater than or less than 1. In this question, f(x) = (0.6)^x represents exponential decay since 0.6 is less than 1.

Creating a Table of Coordinates

To graph a function by hand, select several x-values and compute their corresponding f(x) values. This creates a set of points (x, f(x)) that can be plotted on the coordinate plane. For f(x) = (0.6)^x, choosing integer x-values helps visualize the decay pattern.

Using Graphing Utilities

Graphing utilities, such as calculators or software, allow you to plot functions quickly and accurately. They help confirm the shape and key features of your hand-drawn graph, ensuring correctness and providing a visual check for exponential behavior.