[Highschool - Math 12] Having trouble with a transformation

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  • x After Dawn x
    FFR Veteran
    • Jul 2007
    • 1613
    #1

    [Highschool - Math 12] Having trouble with a transformation

    So I was preparing for my math 12 diploma when I came across this question on a practice exam:

    "The graph of y = f(x) is transformed by reflecting it in the y-axis and then translating it right by 2 units. The equation of the transformed graph is..."

    So I put y = f(-x - 2) because reflecting it over the y-axis means reflecting it horizontally, and translating the graph 2 units to the right means -2. But the answer in the back of the book says the answer is y = -f(x - 2).

    I checked the method that the book uses and they say to replace x with x - 2 (as I did), then replace y with -y to get -y = f(x - 2). Then you divide each side by -1 to get y = -f(x - 2).

    The problem is that these books have a lot of mistakes (there are PLENTY in my other workbooks) and I'm not sure if this is one of them. Can somebody explain to me why we turn y into -y? Wouldn't that turn the y-value of each coordinate into a a negative, and that would reflect it vertically over the x-axis? And if we multiply each side by -1, wouldn't the - in front of the function symbolize a vertical reflection over the x-axis?
    Originally posted by Djr Rap dancer
    Alcohol make peoples retard.
    Drink for forget you are retard and this bring you more retard.
    Just take nicotine patch lol
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    • Patashu
      FFR Simfile Author
      FFR Simfile Author
      • Apr 2006
      • 8609
      #2
      Re: [Highschool - Math 12] Having trouble with a transformation

      reflecting it across the y axis:
      this means that, for instance, the old 1,foo should now occur at -1,foo
      y = f(-x)

      translating it right by two units:
      this means that, for instance, the old 0,foo should now occur at 2,foo and -2,bar occurs at 0,bar
      y = f(-x-2)

      Adding a minus sign outside of the function would, indeed, be flipping it around the x axis. Book's wrong you're right
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        • Zageron
          Zageron E. Tazaterra
          FFR Administrator
          • Apr 2007
          • 6592
          #3
          Re: [Highschool - Math 12] Having trouble with a transformation

          Math 12 is fun stuff.
          Too bad the tests are completely different from the work.

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            • warriormag17
              FFR Veteran
              • Mar 2007
              • 455
              #4
              Re: [Highschool - Math 12] Having trouble with a transformation

              Math 12 = Calc? Confused here. lol

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                • x After Dawn x
                  FFR Veteran
                  • Jul 2007
                  • 1613
                  #5
                  Re: [Highschool - Math 12] Having trouble with a transformation

                  Math 12 = Grade 12 normal math, although I am taking Calculus in grade 12, hehe.

                  But yeah, I don't even know why I made this thread, I went through all of trigonometry and conics today and there are soooooo many mistakes that they're not even a big deal anymore. Apparently 5 x (-5) = 0...
                  Originally posted by Djr Rap dancer
                  Alcohol make peoples retard.
                  Drink for forget you are retard and this bring you more retard.
                  Just take nicotine patch lol

                    Comment

                    • QED Stepfiles
                      FFR Player
                      • Jul 2008
                      • 130
                      #6
                      Re: [Highschool - Math 12] Having trouble with a transformation

                      Well so far everyone has been wrong...

                      Reflecting across the y axis indeed transforms f(x) --> f(-x)

                      Then proceeding to translate two units to the right means that what originally started as (x,f(x)) is now (-x + 2, f(x)). In other words, calling our original function f and our transformed function g, g(-x+2) = f(x)

                      and changing variables y = -x + 2 => x = -y + 2...

                      g(y) = f(-y + 2)

                      The answer is therefore f(-x + 2), not f(-x - 2)

                      Another way to do this is just to remember that you have to put parentheses around the argument when you do the translation, and so it's f(-(x-2)) = f(-x+2). Be careful with this.

                      NB: There's a simple way to do this without thinking it through in the general case. Just check it for the simple line f(x) = x

                      And indeed you'll find that you should get f(x) = -x+2.

                      PS: 5 x (-5) is indeed zero if you're over the correct field =)
                      Last edited by QED Stepfiles; 06-17-2009, 11:21 PM.




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