Question

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

(−3,−10)

(−3,6)

(0,−1)

(−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 for the given \( x \)-values and see if the corresponding \( y \)-values match.

1. For the point \((-3, -10)\):
\[
y = (-3 + 1)^3 - 2 = (-2)^3 - 2 = -8 - 2 = -10
\]
Thus, 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 \( y \)-value does not match; thus, the point \((-3, 6)\) is **not** on the graph.

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

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

From the evaluation, we find that:

- Points on the graph: \((-3, -10)\), \((0, -1)\), and \((-2, -3)\).
- Point not on the graph: \((-3, 6)\).

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