Question

The graph of g(x) is a translation of y = RootIndex 3 StartRoot x EndRoot.
On a coordinate plane, a cube root function goes through (negative 6, negative 2), has an inflection point at (4, 0), and goes through (10, 2).
Which equation represents g(x)?
g(x) = RootIndex 3 StartRoot x minus 4 EndRoot
g(x) = RootIndex 3 StartRoot x + 4 EndRoot
g(x) = RootIndex 3 StartRoot x EndRoot + 1.5
g(x) = RootIndex 3 StartRoot x EndRoot minus 1.5

Answer 1

Given:

A function g(x) is a translation of y = ∛x .

Given g(x) passes through : ( -6 , -2 )  , (10,2)

Has an infection point : (4,0)

To Find:

The equation which best represents g(x) .

Solution:

Given g(x) is a translation of y =∛x

Therefore,

• g(x) = ∛(x + k)

Point of inflection is the point where a change in the direction of curvature occurs.

• g ( -6 ) =  ∛(-6+k) = -2
• Cube = >
• -6 + k = -8
• k = -2 - (1)
• g(x) = ∛x-2

Verifying :

• g(10) = ∛10-2 = ∛8 =2
• Point of inflection = (2,0)

Therefore the equation of g(x) = ∛(x-2)

Answer 2

Answer: The answer is option A

Step-by-step explanation: