Question

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

(-2,-3)
(-3,6)
(0,-1)
(-3,-10)

Answer 1

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

1. For the point \((-2, -3)\):
\[
y = (-2 + 1)^3 - 2 = (-1)^3 - 2 = -1 - 2 = -3
\]
The point \((-2, -3)\) 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 since the calculated y-value is -10, not 6.

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 \((-3, -10)\):
We have already calculated that at \( x = -3 \), \( y = -10 \).
The point \((-3, -10)\) is on the graph.

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