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Reflections of Functions

  1. Nov 3, 2007 #1
    1. The problem statement, all variables and given/known data
    Given f(x)= square root of x - 4, write the equation for -f(x) and f(-x).
    Sketch the three graphs on the same set of axes
    Determine any points that are invariant for each reflection

    3. The attempt at a solution
    well basically I did the first part of the question and the result i got was
    -f(x) = -square root of X + 4
    f(-x) = square root of -x -4

    the second part where it asks to graph these 3 equations, I've graphed the f(x) equation and the -f(x) equation but I can't graph the f(-x) equation. Simply because i get an error when i try to square root a negative number. So how would i graph this kind of eqation?
  2. jcsd
  3. Nov 3, 2007 #2


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    Homework Helper

    ...-f(x) is a reflection in the x-axis
    and f(-x) is a reflection in the y-axis
  4. Nov 3, 2007 #3


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    Staff Emeritus
    Science Advisor

    Do mean f(x)= sqrt(x+ 4) or f(x)= sqrt(x)+ 4?
    If the first, the domain of f is [itex]x+4\ge 0[/itex] or [itex]x \ge -4[/itex] and f(-x) = sqrt(-x+ 4) has domain [itex]-x+4\ge 0[/itex] or [itex]x\le 4[/itex]

    If the second, the domain of f is [itex]x\ge 0[/itex] and f(-x)= sqrt(-x)+ 4 has domain [itex]x\le 0[/itex].

    You have to take values of x in the correct domain in order to graph f(-x). In any case, rock.freak667 is correct: the graph of f(-x) is the refection of the graph of f(x) in the y-axis.
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