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

Question

?(1 point)
Responses

(−3,6)
left parenthesis negative 3 comma 6 right parenthesis

(−3,−10)
left parenthesis negative 3 comma negative 10 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 need to evaluate the function at each x-coordinate of the given points and see if the resulting y-coordinate matches.

1. For the point \((-3, 6)\): \[ y = (-3 + 1)^3 - 2 = (-2)^3 - 2 = -8 - 2 = -10 \] Thus, \((-3, 6)\) does not satisfy the function since \(y \neq 6\).

2. For the point \((-3, -10)\): From the previous calculation, we found: \[ y = -10 \] Therefore, this point satisfies the function.

3. For the point \((-2, -3)\): \[ y = (-2 + 1)^3 - 2 = (-1)^3 - 2 = -1 - 2 = -3 \] This point also satisfies the function.

4. For the point \((0, -1)\): \[ y = (0 + 1)^3 - 2 = (1)^3 - 2 = 1 - 2 = -1 \] This point also satisfies the function.

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