Final answer:
Without specific equations for functions A and F, it is not possible to confirm the exact z-intercepts, y-intercepts, or behavior of the function g represented by S(z) = A(z) - F(z). We would need additional information about the magnitude of A(z) and F(z) over certain intervals to make these determinations.
Step-by-step explanation:
To determine the statements that are true about the function g represented by S(z) = A(z) – F(z), we need to consider the information provided about the functions A and F, as well as how subtraction of functions affects the resulting function's z-intercepts and behavior.
Without specific equations for A(z) and F(z), we cannot ascertain the exact z-intercepts or y-intercepts for S(z). However, we can comment on the behavior of S(z) based on the signs of A(z) and F(z) in certain intervals. If A(z) is greater than F(z) for a range of z values, then S(z) will be positive in that range, and vice versa.
Regarding the z-intercepts: without knowing A(z) and F(z), we cannot confirm where they are. If we had the specific values for A(z) and F(z) at z = 2 and z = -1, we could then confirm or refute these points as z-intercepts.
As for the y-intercept: again, without having the explicit function forms or their evaluations at z = 0, no conclusive statement can be made about whether the y-intercept of S(z) is at (0,-2) or (0,2).
The statements about the values of g being negative when z > 1 or positive when z < -2 are similarly undeterminable without more information about the magnitudes of A(z) and F(z) in those intervals.
In summary, without additional details about the functions A and F, we are unable to confirm or deny any of the statements about the z-intercepts, y-intercepts, or specific behavior of S(z).