Question

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)

Answer 1

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 \( (-3, 6) \).