Label The Exponential Function

Exponential Function Reference This is the general Exponential Function see below for e x f x a x a is any value greater than 0 Properties depend on value of quotaquot When a1, the graph is a horizontal line at y1 Apart from that there are two cases to look at

Study with Quizlet and memorize flashcards containing terms like Which graph represents an exponential function?, Which of the following describes the transformations of gx-2x4 from the parent function fx2x ?, Which function has a range of y lt 3? and more.

Learning Objectives Identify and evaluate exponential functions. Sketch the graph of exponential functions and determine the domain and range. Identify and graph the natural exponential function. Apply the formulas for compound interest.

When exploring linear growth, we observed a constant rate of changea constant number by which the output increased for each unit increase in input. For

Exponential functions are used for many real-world applications such as finance, forensics, computer science, and most of the life sciences. Working with an equation that describes a real-world situation gives us a method for making predictions. Seeing their graphs gives us another layer of insight for predicting future events.

4.2 Applications of Exponential Functions In this section you will learn to find exponential equations using graphs solve exponential growth and decay problems

In the previous examples, we were given an exponential function, which we then evaluated for a given input. Sometimes we are given information about an exponential function without knowing the function explicitly. We must use the information to first write the form of the function, then determine the constants a and b, and evaluate the function.

In this section we will introduce exponential functions. We will be taking a look at some of the basic properties and graphs of exponential functions. We will also discuss what many people consider to be the exponential function, f x ex.

A negative argument results in exponential decay, rather than exponential growth. This means that the graph rapidly decreases towards 0 as x increases. Below is a graph of f x 2 -x. For values of the base between 0 and 1, such as f x 0.3 x, the graph of the exponential function also approaches 0 as x approaches infinity.

An exponential function is one with the form f x abx, where a is the coefficient, b is the base, and x is the exponent. Any exponential function has a domain of all real numbers, but the domain may vary depending on the sign of a. Of course, you can use information about the function such as the asymptote and a few points on the curve to draw the graph of an exponential function.