Which of the following is a point on the graph as described by the function y=(2x+1)cube −4 ?(1 point) Responses (0,−2) left parenthesis 0 comma negative 2 right parenthesis (−1,−3) left parenthesis negative 1 comma negative 3 right parenthesis (1,2) left parenthesis 1 comma 2 right parenthesis (−1,−5)
To find out which of the given points lies on the graph of the function y = (2x+1)^3 − 4, we need to plug the x-values of each point into the function and see if the resulting y-value matches the y-value of the point.
Let's check each point:
1. (0,−2):
For x = 0:
y = (2*0+1)^3 − 4
y = (1)^3 − 4
y = 1 − 4
y = −3
The point (0, −2) does not satisfy the function since we get y = −3, not y = −2.
2. (−1,−3):
For x = −1:
y = (2*(-1)+1)^3 − 4
y = (-2+1)^3 − 4
y = (-1)^3 − 4
y = −1 − 4
y = −5
The point (−1,−3) does not satisfy the function since we get y = −5, not y = −3.
3. (1,2):
For x = 1:
y = (2*1+1)^3 − 4
y = (2+1)^3 − 4
y = (3)^3 − 4
y = 27 − 4
y = 23
The point (1, 2) does not satisfy the function since we get y = 23, not y = 2.
4. (−1,−5):
For x = −1: (We've already calculated this one when checking point 2).
y = (2*(-1)+1)^3 − 4
y = (-1)^3 − 4
y = −1 − 4
y = −5
The point (−1,−5) does satisfy the function since we get y = −5, which matches the y-value of the point.
Therefore, the only point among those given that lies on the graph of the function y = (2x+1)^3 − 4 is (−1,−5).