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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 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.
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 left 3 units and shift up 12 units.

1 answer

To transform \( f(x) = x^2 \) to \( f(x-3) + 12 \), we will break down the transformations step by step.

  1. Transform \( f(x) = x^2 \) to \( f(x-3) \):

    • The expression \( f(x-3) \) represents a horizontal shift to the right by 3 units. So, the first transformation is a shift to the right by 3 units.

  2. Transform \( f(x-3) \) to \( f(x-3) + 12 \):

    • The expression \( f(x-3) + 12 \) represents a vertical shift up by 12 units. So, the second transformation is a shift up by 12 units.

Putting it all together, the order of transformations is: Shift to the right 3 units and shift up 12 units.

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