Transformations question, please help!!?

Just wanted to make sure I was on the right track.

The question is :

The graph of y = sqrt( a - x ) , a > 0 compared to the graph of y = sqrt(x) has what transformations? Describe in words. What transformations have occurred?

I got horizontal reflection with respect to the y - axis and horizontal translation a units to the right.

3 Answers

  • Pope
    Lv 7
    2 months ago
    Favorite Answer

    Yes. Here is how I see it.

    Let f(x) = √(a - x).


    = √[-(-x)]

    = √[a - (a - x)]

    = f(a - x)

    = f[-(x - a)]

    The graph of  y = √(x) is the graph of y = f[-(x - a)].

    Starting from y = f(x), you would effect these transformations in order:

    Scale horizontally with respect to the y-axis by factor -1.

    Translate by vector <a, 0>.

    Those are equivalent to the translations you described.

  • 2 months ago

    y = √(-x) is a reflection in the y-axis

    y = √(a - x) is a horizontal translation of a units to the left


  • sqrt(x)

    sqrt(x - a) would move it a units to the right (since a > 0)

    sqrt(-(x - a)) would flip it horizontally over y = a.

    Just graph it out and see it for yourself.  Pick some arbitrary value for a and graph all 3 functions

    y = x^(1/2)

    y = (x - a)^(1/2)

    y = (a - x)^(1/2)

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