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) = 4^x

Key Concepts

Exponential Functions

Exponential functions are mathematical expressions in the form f(x) = a^x, where 'a' is a positive constant. These functions exhibit rapid growth or decay, depending on whether 'a' is greater than or less than one. Understanding the behavior of exponential functions is crucial for graphing them accurately, as they typically pass through the point (0,1) and increase or decrease steeply.

Table of Coordinates

Creating a table of coordinates involves selecting specific values for 'x' and calculating the corresponding 'f(x)' values. This process helps in plotting points on a graph, providing a visual representation of the function's behavior. For the function f(x) = 4^x, choosing a range of 'x' values, such as -2, -1, 0, 1, and 2, will yield a set of points that illustrate the exponential growth.

Graphing Utilities

Graphing utilities are software tools or calculators that allow users to visualize mathematical functions quickly and accurately. They can confirm hand-drawn graphs by providing precise plots of functions based on input equations. Utilizing a graphing utility for f(x) = 4^x can help verify the shape and key features of the graph, such as intercepts and asymptotic behavior.