Exponential functions are defined as functions with a base raised to an exponent x, were x is the unknown.
Although, there are certain restrictions on the variable a (which is called the base).
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First off, if b is less than 0 the function is known to decay. For example a graph of.png)
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The variable a determines the vertical stretch or compress that the graph will undergo.
The variable c determines the left or right shift that the graph undergoes (+ to x moves left, while - moves right)
The variable d determines the up or down shift of the graph (if d>0 then the graph will shift up d units, if d<0 the graph will shift down d units).
For some longer explanations on graphing or solving.
Although, there are certain restrictions on the variable a (which is called the base).
These restrictions are 
and
and
Or known as
The domain of an exponential function is .png)
The range of an exponential function is.png)
To explain these further, 
because if it did, you would have the graph y=1
because if it did, you would have the graph y=1
If a were to be a negative number, you wouldn't have much of a graph, so you cant have a be negative.
Some basic things that would be good to know are:
Another basic rule to know is that anything raised to the 0 power will equal one.
The parent function known as 
has some basic rules.
has some basic rules.
The y-int. will always be 1, because when x=0 (as said above), y=1.
The horizontal asymptote will be x=0.
And there is no vertical asymptote.
But of course you won't always be dealing with the basic parent function. Here are the modifications you could make to it.
By changing a, b, c and d, you can make the graph either compress, stretch, move left right or up and down.
Notice how the larger b gets the smaller y will be.
Now if .png)
then the graph would look like this. And the larger b gets the steeper the graph would be.
then the graph would look like this. And the larger b gets the steeper the graph would be. .png&container=blogger&gadget=a&rewriteMime=image%2F*)
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Notice how the bigger b is the steeper the graph becomes as you increase x.
The variable a determines the vertical stretch or compress that the graph will undergo.
The variable c determines the left or right shift that the graph undergoes (+ to x moves left, while - moves right)
The variable d determines the up or down shift of the graph (if d>0 then the graph will shift up d units, if d<0 the graph will shift down d units).
For some longer explanations on graphing or solving.
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