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

1 answer

To transform the function \( f(x) = x^2 \) into the form \( f(x - 3) + 12 \), we can follow these steps:

  1. Horizontal Shift: The transformation from \( f(x) \) to \( f(x - 3) \) indicates a shift to the right by 3 units. This is because replacing \( x \) with \( x - 3 \) moves the graph to the right.

  2. Vertical Shift: The addition of 12, specifically in \( f(x - 3) + 12 \), indicates a vertical shift upward by 12 units.

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

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