Final answer:
The question, which asks to identify a function without a -1/2 rate of change, lacks specific functions to analyze but suggests attributes that disqualify a constant rate of change such as being double-valued or divergent.
Step-by-step explanation:
The question presented asks which function does not have a rate of change of -1/2. To determine the rate of change of a function, we typically look at the slope of the line if the function represents a linear relation. For a constant rate of change of -1/2, we would expect a linear function with a slope of -1/2. This means that as we move across 1 unit horizontally, the function should decrease by 1/2 unit vertically. However, without specific functions being provided, we can only speculate about characteristics that would disqualify a function from having a rate of change of -1/2.
From the given references, none of which directly answer the question, some attributes can be considered. The second function is described as being double-valued, which suggests it may not represent a function in the strictest sense, since functions have a single output for each input. The third function is said to diverge and therefore cannot be normalized, which suggests it's not a linear function with a constant rate of change. Functions that diverge typically have rates of change that vary greatly. Finally, functions with discontinuities or those that produce odd functions may not have a constant rate of change, especially if their graphs have breaks or represent higher-level mathematics where the rate of change is not constant over the domain.
Without more context or the functions being spelled out, we cannot definitively say which function does not have the rate of change of -1/2. However, among the options discussed above, functions that diverge, are double-valued, or have discontinuities, are likely candidates for not having a constant rate of change of -1/2.