Question

The graph of g(x) is a reflection and translation of f (x) = RootIndex 3 StartRoot x EndRoot.

On a coordinate plane, a cube root function goes through (0, 1), has an inflection point at (1, 0), and goes through (2, negative 1).

Which equation represents g(x)?

g (x) = RootIndex 3 StartRoot x + 1 EndRoot
g (x) = RootIndex 3 StartRoot x minus 1 EndRoot
g (x) = Negative RootIndex 3 StartRoot x + 1 EndRoot
g (x) = Negative RootIndex 3 StartRoot x minus 1 EndRoot

Answer 1

g(x) = -∛(x − 1)

Reason: the inflection point (1,0) shows the translation is x → x−1, so g(x)=±∛(x−1). Plugging (0,1): ±∛(−1)=±(−1) must equal 1, so choose the negative sign: g(x)=−∛(x−1), which also gives g(2)=−1.