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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 up 12 units.
Shift to the left 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 up 12 units.

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

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

1 answer

To transform \( f(x) = x^2 \) to \( f(x-3) + 12 \), we analyze the transformations step-by-step:

  1. Shift to the right 3 units: The term \( f(x-3) \) indicates a horizontal shift to the right by 3 units. This changes the function from \( f(x) = x^2 \) to \( f(x-3) = (x-3)^2 \).

  2. Shift up 12 units: The \( +12 \) outside of the function signifies a vertical shift upwards by 12 units. This changes the function from \( f(x-3) = (x-3)^2 \) to \( f(x-3) + 12 = (x-3)^2 + 12 \).

Therefore, the correct order of transformations to go from \( f(x) = x^2 \) to \( f(x-3) + 12 \) is:

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

So the correct response is: Shift to the right 3 units and shift up 12 units.