korosh23
  • korosh23
Pre-calculus 12 Question! The zeros of a function y= f(x) are -3 , 0 , 2. Determine the zeros of the function y= f (1 - x). a) -4, -1, 1 b) -3, -1 , 2 c) -2, 1 ,3 d) -1, 1 ,4
Mathematics
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chestercat
  • chestercat
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jim_thompson5910
  • jim_thompson5910
f(1-x) = f(-x+1) f(1-x) = f(-(x-1)) so the graph of f(x) is mirrored over the y axis and we shift 1 unit to the right to get the graph of f(1-x)
korosh23
  • korosh23
@jim_thompson5910 so, the answer is a. Am I right?
korosh23
  • korosh23
-(-3-1)= -4 for the domain?

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jim_thompson5910
  • jim_thompson5910
put another way, if x = -3, then f(-3) = 0 since we're told that -3 is a root so f(1-x) = f(1-(-3)) = f(1+3) = f(4) making 4 a root of f(1-x)
korosh23
  • korosh23
Oh I see now. So any number inside the bracket of f( ) is a root of that function?
jim_thompson5910
  • jim_thompson5910
`The zeros of a function y= f(x) are -3 , 0 , 2` -3 is a root of f(x) 0 is a root of f(x) 2 is a root of f(x)
jim_thompson5910
  • jim_thompson5910
`-3 is a root of f(x)` ----> `f(-3) = 0` `0 is a root of f(x)` ----> `f(0) = 0` `2 is a root of f(x)` ----> `f(2) = 0`
korosh23
  • korosh23
Right, thank you for clarifying it for me. :)
jim_thompson5910
  • jim_thompson5910
sure thing

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