This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up**This preview shows
pages
1–2. Sign up
to
view the full content.*

<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<title>4.1 - Exponential Functions and Their Graphs </title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<link href=".
./m116.css" rel="stylesheet" type="text/css" />
</head>
<body>
<h1>4.1 - Exponential Functions and Their Graphs</h1>
<h2>Exponential Functions</h2>
<p>So far, we have been dealing with algebraic functions. Algebraic functions are
functions which
can be expressed using arithmetic operations and whose values are either rational
or a root of a
rational number.
Now, we will be dealing with transcendental functions.
Transcendental
functions return values which may not be expressible as rational numbers or roots
of rational
numbers.
</p>
<p>Algebraic equations can be solved most of the time by hand.
Transcendental
functions can often
be solved by hand with a calculator necessary if you want a decimal approximation.
However
when transcendental and algebraic functions are mixed in an equation, graphical or
numerical
techniques are sometimes the only way to find the solution.
</p>
<p>The simplest exponential function is:
f(x) = a<sup>x</sup>, a>0,
a≠1
</p>
<p>The reasons for the restrictions are simple.
If a≤0, then when you raise it
to a rational power,
you may not get a real number.
Example: If a=-2, then (-2)<sup>0.5</sup> = sqrt(-
2) which isn't real.
If a=1,
then no matter what x is, the value of f(x) is 1.
That is a pretty boring
function, and it is certainly
not one-to-one.
</p>
<p>Recall that one-to-one functions had several properties that make them
desirable.
They have
inverses that are also functions.
They can be applied to both sides of an
equation.</p>
<h2>Graphs of Exponential Functions</h2>
<p><img src="2x.gif" alt="y=2^x" width="218" height="277" class="imgrt" />The graph
of y=2<sup>x</sup> is shown to the right.
Here are some
properties of the exponential function when the base is
greater than 1.
</p>

This
** preview**
has intentionally

This is the end of the preview. Sign up
to
access the rest of the document.

4.1 - Exponential Functions and Their Graphs -

View Full Document

Ask a homework question
- tutors are online