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functions and piece wise functions

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when you find the domain, think of x values that cant be plugged in
 
in this instance, the denominator (bottom) cant be = 0
 
so x^2-7x-8 =0  this will tell you the #'s you cant use.
 
(x-8)(x+1) = 0
x=8 and -1
 
so you domain would be all real numbers such that x doesnt equal 8 or -1