What is the order of combinations to transform f(x)=x^2

Question

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.

Answer 1

To transform the function \( f(x) = x^2 \) to \( f(x - 3) + 12 \), we need to consider a two-step process in terms of transformations.

1. Shift to the right by 3 units: The expression \( f(x-3) \) means we are replacing \( x \) with \( x - 3 \). This is a horizontal shift to the right by 3 units.

2. Shift up by 12 units: The \( +12 \) outside the function indicates a vertical shift upwards by 12 units.

So the correct order of transformations is:

• Shift to the right 3 units
• Shift up 12 units

Thus, the correct response is:

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