![]() We’ll use the function g ( x ) = ( 1 2 ) x. To get a sense of the behavior of exponential decay, we can create a table of values for a function of the form f ( x ) = b x Is all real numbers, the range is ( 0, ∞ ) , shows the exponential growth function f ( x ) = 2 x. Increases, the output values increase without bound andĭecreases, the output values grow smaller, approaching zero. the output values are positive for all values of.This means that as the input increases by 1, the output value will be the product of the base and the previous output, regardless of the value of a. In fact, for any exponential function with the form f ( x ) = a b x, b xĮach output value is the product of the previous output and the base, 2. Observe how the output values in change as the input increases by 1. Recall the table of values for a function of the form f ( x ) = b x Graphing Exponential Functionsīefore we begin graphing, it is helpful to review the behavior of exponential growth. It gives us another layer of insight for predicting future events. We learn a lot about things by seeing their pictorial representations, and that is exactly why graphing exponential equations is a powerful tool. ![]() Most of the time, however, the equation itself is not enough. Working with an equation that describes a real-world situation gives us a method for making predictions. Graph exponential functions using transformations.Īs we discussed in the previous section, exponential functions are used for many real-world applications such as finance, forensics, computer science, and most of the life sciences.
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