Question

For which pair of functions is the vertex of g(x) 3 units to the right of the vertex of f(x)?

Answer 1

Answer: A.

`f(x)=x^2\text{ and }g(x)=(x-3)^2`

Step-by-step explanation

Given:

`f(x)=x^2`

As we want to move the vertex 3 units to the right, this means we have to make a transformation on x (not y). Then, we have to make x = 3 when y = 0, meaning:

`\begin{gathered} x=3 \\ x-3=0 \end{gathered}`

Thus:

`g(x)=(x-3)^2`

We have to subtract 3 inside the parenthesis because if we add/subtract 3 outside, it would have an impact on y.