Final answer:
The y-intercept of the equation −1/2(x−1)³+2 is (0, 1). The correct answer is b) (0, 1).
Step-by-step explanation:
To find the y-intercept of the equation, we set x = 0 and solve for y.
Substituting x = 0 into the equation -1/2(x-1)^3 + 2, we get:
-1/2(0-1)^3 + 2 = -1/2(1)^3 + 2 = -1/2 + 2 = 2 - 1/2 = 3/2 = 1.5.
Therefore, the y-intercept of the equation is (0, 1.5), which corresponds to option b) (0, 1) in the answer choices.
These intercepts hold significance in understanding the behavior of functions or models. In linear equations, intercepts provide critical information about the behavior of the graph, while in statistics, intercepts represent a starting point or a baseline for the regression line, showcasing the value of the dependent variable when independent variables are zero.