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

Question

to f(x−3)+12

Responses

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 left 3 units and shift up 12 units.

Shift to the left 3 units and shift down 12 units.

Answer 1

To transform \( f(x) = x^2 \) into \( f(x-3) + 12 \), we need to analyze the transformations step by step.

1. Shift to the right by 3 units:

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

2. Shift up by 12 units:

   • The addition of 12 in \( f(x-3) + 12 \) means we are raising the entire graph up by 12 units.

Putting both transformations together, we first shift the graph of \( f(x) = x^2 \) to the right by 3 units, and then we shift it up by 12 units.

Therefore, the correct response is: Shift to the right 3 units and shift up 12 units.