Final answer:
To calculate the rate of change, the change in y is divided by the change in x; however, the data provided appears to contain an error, and the calculated rate of change does not match any of the options provided.
Step-by-step explanation:
To calculate the rate of change of a function described by data points, you can simply use the formula (change in y) / (change in x). However, the given data points (x, y) from the question (-1, 5), (2, -4), and (7, -1910) seem inconsistent and likely contain an error. Typically, the data should consistently reflect the type of function whether it be linear, quadratic, etc., but an immense drop from -4 to -1910 is indicative of an error in the dataset.
If we were to ignore the apparent error and proceed, we would take two points to calculate the rate of change. For instance, using points (2, -4) and (7, -1910), we would have: Rate of change = (-1910 - (-4)) / (7 - 2) = -1906 / 5 = -381.2, which is not one of the options provided in the question.
Given that none of the provided options (A. -3, B. 4, C. -9, D. 6) are even near the value of -381.2, and considering the irregularity of the function's behavior as per the numbers provided, further clarification of the correct dataset is required to provide an accurate calculation of the rate of change.