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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 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 down 12 units.

3 answers

To transform \( f(x) = x^2 \) to \( f(x - 3) + 12 \), we can break it down into two steps:

  1. Horizontal Shift: The term \( f(x - 3) \) represents a horizontal shift. Specifically, replacing \( x \) with \( x - 3 \) shifts the graph 3 units to the right. So, this step translates the graph of \( f(x) \) to the right by 3 units.

  2. Vertical Shift: The "+12" outside the function indicates a vertical shift. Adding 12 to the function shifts the graph up by 12 units.

Putting it together, the correct order is:

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

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

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