Exponential Functions

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In this section, we will learn about exponential functions. Exponential functions are of the form: f(x) = ax, where a > 0, a ≠ 1, and x is any real number. We begin by learning how to graph an exponential function. To perform this operation, we create enough ordered pairs for a good picture. We then plot the ordered pairs and sketch the graph. Ideally, we would like to graph functions of this form using a graphing calculator or graphing software. We then move on to learn how to solve exponential equations of the form: ax = ay : when a > 0 and a ≠ 1, then x = y. We can use this property to set up the following steps. First, each side must have the same base. If the two sides do not have the same base, we express each as a power of the same base. Second, we simplify the exponents as much as possible. Third, we set the exponents equal to each other and solve the resulting equation. Fourth and final, we check our answer in the original equation.
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