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

(−2,−3)
left parenthesis negative 2 comma negative 3 right parenthesis

(0,−1)

Answer 1

To determine which point does not belong to the graph of the function \( y = (x + 1)^3 - 2 \), we can evaluate the function at each \( x \) value given in the response options and compare the results to the corresponding \( y \) values in the points.

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

2. **For the point \((-3, 6)\)**:
\[
y = (-3 + 1)^3 - 2 = (-2)^3 - 2 = -8 - 2 = -10
\]
The \( y \) value should be \(-10\), so this point is **not** on the graph.

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

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

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