Question

The function below has been transformed from f(x) = x2. Describe the transformation. h(x) = 4x2 + 12

Answer 1

Answer:

• vertically expanded by a factor of 4
• then, translated upward 12 units

Step-by-step explanation:

If f(x) = x² and g(x) = 4x² = 4f(x), the function g(x) represents a vertical expansion of f(x) by a factor of 4.

If h(x) = g(x) +12, the function h(x) represents a translation of g(x) by 12 units upward.

Together, these transformations on f(x) are ...

• vertical expansion by a factor of 4
• translation upward by 12 units

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Please be aware that there are alternate transformations that will do the same thing:

  h(x) = 4(f(x) +3) . . . . is a translation upward by 3, then a vertical expansion by a factor of 4

  h(x) = f(2x) +12 . . . . is horizontal compression of f(x) by a factor of 2, then a translation upward by 12.