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What is the order of combinations to transform f(x)=x2

to f(x−3)+12
?(1 point)
Responses

Shift to the left 3 units and shift down 12 units.
Shift to the left 3 units and shift down 12 units.

Shift to the right 3 units and shift up 12 units.
Shift to the right 3 units and shift up 12 units.

Shift to the right 3 units and shift down 1

1 answer

To analyze the transformation of the function \( f(x) = x^2 \) to \( f(x - 3) + 12 \), we can break it down into two steps.

  1. Horizontal Shift: The expression \( f(x - 3) \) translates to a horizontal shift of the function \( f(x) \). Specifically, "subtracting 3 from the input \( x \)" means that the graph of \( f(x) \) will move to the right by 3 units.

  2. Vertical Shift: The "+ 12" after \( f(x - 3) \) means that the entire function is then shifted upwards by 12 units.

Thus, the correct order of transformations from \( f(x) = x^2 \) to \( f(x - 3) + 12 \) is to shift to the right 3 units, and then shift up 12 units.

Based on this analysis, the correct response is:

Shift to the right 3 units and shift up 12 units.