8a)++Graphs+of+exponential+functions

An exponential function is used today for changes in population or in prices etc... An exponential function has the form y=ab^x where (a) doesn't equal 0 and the base (b) is a positive number other than 1. If a > 0 and b > 1, then the function y=ab^x is an exponential growth function, and b is called the growth factor. The simplest type of exponential growth function has the form y=b^x. Also when 0 < b < 1, then the function y=ab^x is a exponential decay. The base (b) of the exponential decay function is called the decay factor. When the function is of the form y=ab^x, the y intercept is (a).

In an exponential growth graph you can see that as the x increases the y increases, and for the exponential decay graph you can see as the x increases the y decreases. For the domain and range of the exponential graphs. Both the domains of an exponential growth and exponential decay are all real numbers but the ranges are different. The range for an exponential decay and exponential growth can be y 0.

For increasingly negative values of x growth functions get closer to y = 0, but never reach y = 0. The same for increasingly positive values of x, decay function get closer to y = 0, but never reach y = 0. This equation y = 0 is called an asymptote. As you can tell an asymptote is a line in a graph that approaches more and more closer, but never hits the x axis. Also there are times where you must translate the original x and y intercepts when y= ab^(x-h) + k where the h affects the x intercept and the k affects the y intercept.

[|Graphing Exponential Fuctions: Intro]

[|Graphing Exponential Functions]



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 * Problem: Graph //f(x) = 2x//.

Solution:** Plug in numbers for //x// and find values for //y//, as we have done with the table below.

_____________________           | x | 0 | 1 | 2 | 3 | -           | y | 1 | 2 | 4 | 8 | -

Now plot the points and draw the graph (shown below). code 

f is a function - f (x) = 2(x - 2)


 * 1) To find the x intercept we need to solve the equation - f(x) = 02(x - 2) = 0

(4,4) (-1,1/8) > >
 * 1) Plug in points for X and solve the equation for y
 * 1) Let us now use all the above information to graph f.

Consider the graph of //f//( //x//) = 2 //x// in Figure 1, plotted by substituting a small collection of integers into //f//.

From the table, it is clear why the graph of //f// gets closer and closer to the //x//-axis as //x// gets more and more negative. Since a negative input becomes a negative exponent, your result will be a fraction. The larger the negative input, the smaller the value of the fraction. However, once the inputs become positive, the graph grows quickly.
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 * [[image:http://media.wiley.com/Lux/28/10728.nfg001.jpg align="absMiddle"]] ||
 * [[image:http://media.wiley.com/Lux/28/10728.nfg001.jpg align="absMiddle"]] ||