Question

Which graph represents y = RootIndex 3 StartRoot x minus 5 EndRoot?
1. On a coordinate plane, a cubic function has a point of inflection at x = 0 and crosses the x-axis at x = 5.
2. On a coordinate plane, a cubic function has a point of inflection at x = negative 5 and crosses the x-axis at x = 2.
3. On a coordinate plane, a cubic function has a point of inflection at y = negative 5 and crosses the x-axis at y = negative 5.
4. On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5.

Answer 1

Answer: 4.

Reason: y = ∛(x − 5) is the cube-root graph shifted right 5 units. The x-intercept occurs where ∛(x − 5) = 0 → x = 5, and the point of inflection (originally at (0,0) for y = ∛x) is shifted to (5,0). Option 4 matches.