Question

The graph of y = RootIndex 3 StartRoot x minus 3 EndRootis a horizontal translation of y = RootIndex 3 StartRoot x EndRoot. Which is the graph of y = RootIndex 3 StartRoot x minus 3 EndRoot?

On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (2.5, 0), and goes through (10, 2).
On a coordinate plane, a cube root function goes through (negative 10, negative 2), has an inflection point at (negative 3, 0), and goes through (4, 2).
On a coordinate plane, a cube root function goes through (negative 10, 1), has an inflection point at (0, 3), and goes through (8, 5).
On a coordinate plane, a cube root function goes through (negative 8, negative 5), has an inflectoin point at (0, negative 3), and goes through (8, negative 1).

Answer 1

The fourth graph.

Reason: y = ∛x − 3 is the graph of y = ∛x shifted down 3. ∛x has inflection at (0,0) and goes through (−8,−2) and (8,2). Subtracting 3 gives inflection (0,−3) and the points (−8,−5) and (8,−1), which matches the fourth description.