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Math Help - transfromations of an exponential function??

  1. #1
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    Question transfromations of an exponential function??

    Consider the graph of y = ex. (a) Find the equation of the graph that
    results from reflecting about the line y = 8.

    y = 1
    _________________________

    (b) Find the equation of the graph that results from reflecting about
    the line x = 2.

    y =_____________________________

    2
    How would i solve this, and can u show the steps?
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  2. #2
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    Hello Sneaky
    Quote Originally Posted by Sneaky View Post
    Consider the graph of y = ex. (a) Find the equation of the graph that
    results from reflecting about the line y = 8.
    Suppose that the point (x_1, y_1) is transformed into the point (x_2, y_2), by a reflection in the line y = 8. Then, since the reflection line is horizontal, the x-coordinate doesn't change, and so:

    x_2 = x_1 (1)

    The fundamental property of a reflection is that the distances of a point and its reflection from the mirror-line are equal. Let's assume (and it won't make any difference if it's the other way around) that y_1 < 8 and y_2 > 8. Then these distances are (8-y_1) and (y_2-8), respectively. So

    8-y_1 = y_2-8

    \Rightarrow y_2 = 16-y_1 (2)

    So, since y_1 = e^{x_1}, the equation relating y_2 and x_2, when we use (1) and (2), is:

    y_2 = 16 - e^{x_2}

    and so the equation of the reflected graph is

    y =  16-e^x


    (b) Find the equation of the graph that results from reflecting about
    the line x = 2.

    y =_____________________________

    2
    How would i solve this, and can u show the steps?
    Do this in the same way. Assume that (x_1,y_1)\rightarrow (x_2,y_2). Then, since the mirror-line is vertical

    y_2=y_1

    and this time it's the horizontal distances from the mirror-line that are equal. So

    2-x_1 = x_2-2

    \Rightarrow x_1 = 4-x_2

    And, once again, y_1=e^{x_1}, so how are y_2 and x_2 related? This will then give you the equation of the transformed graph.

    Can you complete this now?

    Grandad
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