Ricardo transformed the quadratic parent function f(x) to create g(x). After the
transformation, he noticed that the domain
and range were the same for f(x) and g(x).
Which of the following could NOT represent
g(x)?
A. g(x) = f(x + 5)
B. g(x) = f(x) + 5
C. g(x) - 5f(x)
D. g(x) = f(5x)

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.