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The function g(x) = (x + 2)^2 + 4 is a transformation of the parent function f(x) = x^2. Select all the...

The function g(x) = (x + 2)^2 + 4 is a transformation of the parent function f(x) = x^2. Select all the statements that are true about the transformation.
□ Function g is the result of f being translated right 2 units and down 4 units.
□ Function g is the result of f being translated left 2 units and up 4 units.
□ The graph of function f opens upward.
□ The graph of function g opens downward.
□ The graph of function f is compressed by a factor of 2.

Answer

  1. False: Function g is not the result of f being translated right 2 units and down 4 units. It is translated left 2 units and up 4 units.

  2. True: Function g is the result of f being translated left 2 units and up 4 units.

  3. True: The graph of function f opens upward, as it is a standard parabola.

  4. False: The graph of function g does not open downward; it opens upward.

  5. False: The graph of function f is not compressed by a factor of 2; there is no compression or stretching involved in this transformation.

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