Question

Which of the following points does not belong to the graph of the function y=(x+1)3−2 ?(1 point) Responses (−3,−10) left parenthesis negative 3 comma negative 10 right parenthesis (−3,6) left parenthesis negative 3 comma 6 right parenthesis (0,−1) left parenthesis 0 comma negative 1 right parenthesis (−2,−3)

Answer 1

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

1. **For the point \((-3, -10)\)**:
\[
y = (-3 + 1)^3 - 2 = (-2)^3 - 2 = -8 - 2 = -10
\]
The point \((-3, -10)\) is on the graph.

2. **For the point \((-3, 6)\)**:
\[
y = (-3 + 1)^3 - 2 = (-2)^3 - 2 = -8 - 2 = -10
\]
The point \((-3, 6)\) is NOT on the graph.

3. **For the point \((0, -1)\)**:
\[
y = (0 + 1)^3 - 2 = (1)^3 - 2 = 1 - 2 = -1
\]
The point \((0, -1)\) is on the graph.

4. **For the point \((-2, -3)\)**:
\[
y = (-2 + 1)^3 - 2 = (-1)^3 - 2 = -1 - 2 = -3
\]
The point \((-2, -3)\) is on the graph.

Thus, the point that does NOT belong to the graph of the function \(y = (x + 1)^3 - 2\) is \((-3, 6)\).