Mickey1012
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Margo is comparing the functions f(x) = |x| and g(x) = |x + 1| - 5. She said the graph of g is a vertical translation of the graph of f 5 units down and a horizontal translation of the graph of f 1 unit right. What is Margo's error?

Respuesta :

Given function in the question is,

  • f(x) = |x|
  • Image function after horizontal and vertical translations,

        g(x) = |x + 1| - 5

Rules to remember for the translation a function,

  • If the function 'f' is translated 'h' units right, the image function will be,

        g(x) = |x - h|

  • If the function 'f' is translated 'h' units left, the image function will be,

        h(x) = |x + h|

  • If a function 'f' is translated 'k' units up, the image function will be,

        k(x) = |x| + k

  • If a function 'f' is translated 'k' units down, image function will be,

        p(x) = |x| - k

Using these rules,

Function 'f' will be translated 1 units left and and 5 units down to form the image function 'g'.

       Therefore, Margo made an error to interpret that the function is translated 1 units right.

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