Hi! I wrote this talk to encourage the early use of the words and meaning of identity, opposite, and reciprocal functions in the teaching
of algebra and prealgebra and to provide the support material to promote student success and faculty satisfaction on a job well done.
 Agnes (A^{2}) Azzolino

function name  symbol  meaning/performance/action 



identity  x  no change, no sign change, no size change,
exactly the same as the input, identically the same 

opposite  x  sign change, no size change, the additive inverse 

reciprocal  1/x, x^{1} 
no sign change, size change, the multiplicative inverse
 if x>1, the reciprocal is smaller than x and positive
 if x=1, the reciprocal is x, 1, still positive
 if 0 if x=0, the reciprocal infinite in size, is undefined
 if 1 if x=1, the reciprocal is x, 1, still negative
 if x<1, the reciprocal is smaller in magnitude and negative 

In short:  
identity  no change  
opposite  sign change  
reciprocal  size change 
