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Exponentials and Logarithms

The important thing to remember for these graphs is the basic shape.

Remember that exponentials have

f( x ) = a^x ... the a is a base ... x is the variable in the exponent
 
 
Whena > 1(likef( x ) = 2^xorf( x ) = e^x),
the basic shape of the graph looks like

 

the basic shape of the graph f( x ) = a^x when a > 1


The bigger x
gets, the faster
the graph climbs
The x-axis is a horizontal asymptote. 

 

When0 < a < 1(likef( x ) = ( 1 / 3 )^x), the basic shape
goes downhill:

the basic shape of the graph f( x ) = a^x when 0 < a < 1