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 down 12 units.
Shift to the right 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 down 12 units.
Shift to the left 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 analyze what's happening in each part of the transformation.

1. Starting with \( f(x) = x^2 \):

   • This is the original function.

2. Transforming to \( f(x - 3) \):

   • The expression \( f(x - 3) \) means we are replacing \( x \) with \( x - 3 \).
   • This transformation shifts the graph to the right by 3 units.

3. Adding 12:

   • The \( + 12 \) indicates a vertical shift.
   • This shifts the graph up by 12 units.

Combining these two transformations, the order is:

• Shift to the right 3 units (first), and then
• Shift up 12 units (second).

Thus, the correct response is:

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