What is the order of combinations to transform f(x)=x2

Question

𝑓
(
𝑥
)
=
𝑥
2
to f(x−3)+12
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.

Answer 1

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

1. Shift the function: The expression \( f(x-3) \) indicates a horizontal shift. Specifically, replacing \( x \) with \( x-3 \) shifts the graph to the right by 3 units.

2. Vertical shift: The addition of 12, as in \( +12 \), indicates a vertical shift upward by 12 units.

Therefore, the correct combination of transformations is:

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