The graph of h(x) is a translation of f (x) = RootIndex 3 StartRoot x EndRoot. On a coordinate plane, a cube root function goes through (negative 3, negative 1), has an inflection point at (negative 2, 0), and goes through (negative 1, 1). Which equation represents h(x)?

The correct option is;

Step-by-step explanation:

Given that h(x) is a translation of f(x) = ∛x

From the points on the graph, given that the function goes through (-1, 1) and (-3, -1) we have;

When x = -1, h(x) = 1

When x = -3, h(x) = -1

h''(x) = (-2, 0)

Which gives  

d²(∛(x + a))/dx²= , have coordinates (-2, 0)

When h(x) = 0, x = -2 which gives;

Therefore, a = (0/(-2/9))^(-3/5) + 2

a = 2

The translation is h(x) =

We check, that when, x = -1, y = 1 which gives;

h(x) = which satisfies the condition that h(x) passes through the point (-1, 1)

For the point (-3, -1), we have;

h(x) =

Therefore, the equation, h(x) = passes through the points (-1, 1) and (-3, -1) and has an inflection point at (-2, 0).

were is the equation