Final answer:
Roots of the function f(x) = |x + 3| - 4 are x = 1 and x = -7. The y-intercept of this function is at -1. The y-intercept is significant when interpreting the best-fit line in linear regression analysis.
Step-by-step explanation:
The question given is to find the root and y-intercept for the function f(x) = |x + 3| - 4.
To find the root, we set the function equal to zero and solve for x: |x + 3| - 4 = 0, which gives us x + 3 = 4 or x + 3 = -4, leading to two roots: x = 1 and x = -7.
To find the y-intercept, we evaluate f(0), which gives us |0 + 3| - 4 = -1. Thus, the y-intercept is -1.
Understanding and interpreting the y-intercept involves recognizing that it is the value of f(x) when x is zero. This is crucial in linear regression analysis, where the y-intercept gives the best value of the relationship when x is zero.
In some contexts, the y-intercept has practical implications, like representing initial conditions in a time-dependent scenario.