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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 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 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 down 12 units.

1 answer

To transform the function \( f(x) = x^2 \) to \( f(x-3) + 12 \), we need to analyze the changes made to the function:

  1. Horizontal Shift: The expression \( f(x-3) \) indicates that we are shifting the function \( f(x) \) to the right by 3 units. This follows the general rule for horizontal shifts, where \( f(x - c) \) shifts the graph to the right by \( c \) units.

  2. Vertical Shift: After applying the horizontal shift, the additional \( +12 \) indicates that we are shifting the entire graph up by 12 units.

Putting it together:

  • Shift right by 3 units.
  • Then, shift up by 12 units.

Thus, the correct response is:

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