1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook