Which of the following points does not belong to the graph of the function y=(x+1)3−2

?(1 point)
Responses

(0,−1)
left parenthesis 0 comma negative 1 right parenthesis

(−3,−10)
left parenthesis negative 3 comma negative 10 right parenthesis

(−3,6)
left parenthesis negative 3 comma 6 right parenthesis

(−2,−3)

1 answer

To determine which of the provided points does not belong to the graph of the function \( y = (x + 1)^3 - 2 \), we will evaluate the function at the x-coordinates of each point and see if the corresponding y-coordinate matches.

  1. For the point \( (0, -1) \): \[ y = (0 + 1)^3 - 2 = 1^3 - 2 = 1 - 2 = -1 \] This point belongs to the graph.

  2. For the point \( (-3, -10) \): \[ y = (-3 + 1)^3 - 2 = (-2)^3 - 2 = -8 - 2 = -10 \] This point belongs to the graph.

  3. For the point \( (-3, 6) \): \[ y = (-3 + 1)^3 - 2 = (-2)^3 - 2 = -8 - 2 = -10 \] This point does not belong to the graph, as the y-coordinate should be -10.

  4. For the point \( (-2, -3) \): \[ y = (-2 + 1)^3 - 2 = (-1)^3 - 2 = -1 - 2 = -3 \] This point belongs to the graph.

Thus, the point that does not belong to the graph is \( (-3, 6) \).