Solve. 5. The graph of f(x)= x is reflected across the x-axis. The graph is then translated 11 units up and 7 units to the left.

Question

Solve.
5. The graph of f(x)= x is reflected across the x-axis. The graph is then
translated 11 units up and 7 units to the left. Write the equation of the
transformed function.

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Khoii Minh 4 years 2021-09-05T09:39:58+00:00 1 Answers 37 views 0

Answers ( )

  1. hongcuc2
    0
    2021-09-05T09:41:21+00:00
    Reply

    Given:

    The function is:

    f(x)=x

    The graph of this function reflected across the x-axis. The graph is then  translated 11 units up and 7 units to the left.

    To find:

    The equation of the transformed function.

    Solution:

    The translation is defined as

    g(x)=kf(x+a)+b                …. (i)

    Where, k is stretch factor, a is horizontal shift and b is vertical shift.

    If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

    If k<0, then the graph is reflected across the x-axis.

    If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

    If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

    The graph of this function reflected across the x-axis. The graph is then  translated 11 units up and 7 units to the left.  So, k=-1, b=11, a=7. Putting these value in (i), we get

    g(x)=(-1)f(x+7)+11

    g(x)=-(x+7)+11                     [\because f(x)=x]

    g(x)=-x-7+11

    g(x)=-x+4

    Therefore, the required function is g(x)=-x+4.

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