Determine the average rate of change for the function.
-p(x)= -x + 4
A)-1
B)1
C)- 4
D)4

Question

Quizplus · Accepted Answer

The average rate of change for p(x) can be found by taking the difference of p(x) between two values of x and dividing by the difference in x. For example, if we choose x=1 and x=3, the difference in p(x) would be (-1+4) - (-3+4) = 2, and the difference in x would be 2. Therefore, the average rate of change would be 2/2 = 1. Since the coefficient of x is -1, this means that the function is decreasing by 1 for every 1 unit increase in x. Therefore, the best choice is A) -1. The average rate of change of p(x) over an interval [a,b] is given by:

average rate of change = (p(b) - p(a))/(b - a)

For the given function p(x) = -x + 4, we have:

average rate of change = (p(b) - p(a))/(b - a) 
= (-b + 4 - (-a + 4))/(b - a) 
= (-b + a)/(b - a) 
= -1

Therefore, the average rate of change of p(x) is -1. The best choice is A).

Determine the Average Rate of Change for the Function