Final answer:
Given the average rate of change and the value of g(-2), we calculated g(6) using the average rate of change formula and found it to be 11. This value was not among the provided options, suggesting a possible error in the question or options.
Step-by-step explanation:
The student is asked about the value of the function g(x) at a particular point when they are given that g(-2) = -7 and the rate of change of 2.25 over the interval -2 < x < 6. To find the value of g(6), you can use the definition of average rate of change, which is similar to the slope of a line in the interval.
The average rate of change formula is:
(g(b) - g(a)) / (b - a) = rate of change
Here, a = -2, b = 6, and the given rate of change is 2.25. We already know g(a) = g(-2) = -7. By substituting these values into the formula, we get:
(g(6) - (-7)) / (6 - (-2)) = 2.25
(g(6) + 7) / 8 = 2.25
g(6) + 7 = 2.25 * 8
g(6) + 7 = 18
g(6) = 18 - 7
g(6) = 11
So the value of g(6) is not available in the given options A. -6, B. -5, C. -4, or D. -3. There might be a typo in the options provided, or perhaps an error in the question, as our calculation yields a value of 11 for g(6).