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Determine the equation of g(x) that results from translating the function f(x) = (x + 10)2 to the right 13 units.

g(x) = (x - 3)2

g(x) = (x + 23)2

g(x) = (x + 10)2 - 13

g(x) = (x + 10)2 + 13
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1 Answer

The rules are:
  1. f(x+c) translates f(x) c units to the left
  2. f(x-c) translates f(x) c units to the right
 
You want to translate f(x) 13 units to the right, so use rule 2 with c = 13:
 
g(x) = f(x-13)
 
Just replace the x in f(x) with x-13:
 
g(x) = f(x-13) = (x-13+10)2 = (x-3)2