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Exponential Functions

Exponential Functions

Exponential Functions

In this chapter, expressions with exponents are explored. The aspects that are looked into include Properties of Exponents and how to write radicals using rational exponents.
The Properties of Exponents are a set of tools that can be used to rewrite and simplify expressions with exponents.
By showing that it is possible rewrite expressions written as radicals into expressions with rational exponents allows for the Properties of Exponents to be used to understand and manipulate radical expressions.
Also in this chapter exponential functions are studied. Here the function rules and graphs are investigated, it is shown that growth and decay functions can be written using exponential functions and how to transform an exponential function's function rule and how it affects its graph.
Specifically, exponential functions are contrasted with linear functions. Rather than having a constant rate of change as linear functions do, exponential functions are shown to change by a constant multiplier.
There are several different methods how to graph exponential functions. One is to use a table of values and another is to use the function rule. The graphs of exponential functions can be used to solve exponential equations.
Exponential growth functions and exponential decay functions are used to analyze and understand situations in context.
The transformations on exponential functions that are explored in the chapter include translations, reflections, stretches, and shrinks.

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