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1-94.

If f(x) = (x – 3)2 + 4 and g(x) = − 2, write explicit equations for the following transformations. Homework Help ✎

  1. h(x) = f(x + 2) – 5

    h(x) = f(x + 2) = 5
    h(x) = [((x + 2) − 3) 2] + 4 − 5
    Simplify.

  2. k(x) = g(3 – x) + 2

    (3 − x), the horizontal shift, will replace 'x' in the g(x) function.
    +2, the vertical shift, will be added to the entire 'g(x)' function.

  3. Use set notation to state the domains and ranges of h and k.

    Consider the parent graphs of f and g.
    Domain and range will shift from that of the parent.
    The parent graph of f(x) is y = x².
    What is the parent graph of g(x)?