Which of the following functions have an average rate of change that is positive on the interval from x=
–
3 to x=
–
1?
To determine which functions have a positive average rate of change on the interval from x = -3 to x = -1, we need to calculate the slope of each function over that interval.
The average rate of change of a function f(x) over an interval [a, b] is given by the formula:
Average Rate of Change = (f(b) - f(a))/(b - a)
Let's calculate the average rate of change for each function over the interval from x = -3 to x = -1:
1. Take a function, substitute -3 for a, and -1 for b in the formula. Calculate the value of the function at those points.
2. Subtract the value of f(x) at -3 from the value of f(x) at -1.
3. Divide the difference by the difference between -1 and -3.
By comparing the calculated average rates of change, we can determine which functions have a positive average rate of change on the given interval.