The interval for which the average rate of change of f(x) is negative is; from x = 0 to x = 2.5.
For the average rate of change of f(x) to be negative, it means that the change in y and the change in x must have opposite signs.
For example, if the change in y is negative, them the change in x must be positive.
Similarly, if the change in y is positive, then change in x must be negative.
Now, the graph showing this quadratic function is missing and so i have attached it.
From the graph, the only interval at which the rate of change for y and x have opposite signs is from x = 0 to x = 2.5.
In this interval, we see that x is increasing from 0 to 2.5 which is positive change while y is decreasing from 1 to -3 which is negative change.
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