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. f(x) = (0.6)^x

Key Concepts

Exponential Functions

Exponential functions are mathematical expressions in the form f(x) = a^x, where 'a' is a positive constant. In this case, f(x) = (0.6)^x represents a decreasing exponential function because the base (0.6) is less than 1. Understanding the behavior of exponential functions is crucial for predicting how they grow or decay as 'x' changes.

Graphing Functions

Graphing functions involves plotting points on a coordinate plane to visualize the relationship between the input (x) and output (f(x)). For the function f(x) = (0.6)^x, creating a table of coordinates helps identify key points, such as f(0) = 1 and f(1) = 0.6, which are essential for accurately sketching the graph.

Using Graphing Utilities

Graphing utilities, such as graphing calculators or software, provide a powerful way to visualize functions quickly and accurately. They can confirm the hand-drawn graph by generating a precise representation of the function. Utilizing these tools can help students verify their work and understand the function's behavior more deeply.