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Exponentials and Logarithms

So, what if there is a negative exponent?  Does the graph go uphill?  Downhill?  It all depends on the base!
f( x ) = 2^( -x )is reallyf( x ) = ( 1 / 2 )^x     Do the Algebra!

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

 

f( x ) = ( 1 / 4 )^( -x )is reallyf( x ) = 4^x

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