Compare the average rates of change for the graphed square root function p(x)=x+4−−−−√ and the cube root function f(x)=x+4−−−−√3 over the interval [−4,−3].
The functions have the same average rate of change of 0.
The cube root function has the greater average rate of change.
The square root function has the greater average rate of change.
The functions have the same average rate of change of 1.
To find the average rate of change of a function over an interval, we can use the formula:
Average Rate of Change = (f(b) - f(a))/(b - a)
For the given interval [-4, -3]:
For p(x) = x+4^0.5
p(-4) = -4 + 4^0.5 = -4 + 2 = -2
p(-3) = -3 + 4^0.5 = -3 + 2 = -1
Average rate of change for p(x) = (-1 - (-2))/(-3 - (-4)) = 1/1 = 1
For f(x) = x+4^1/3
f(-4) = -4 + 4^1/3 = -4 + 2 = -2
f(-3) = -3 + 4^1/3 = -3 + 2 = -1
Average rate of change for f(x) = (-1 - (-2))/(-3 - (-4)) = 1/1 = 1
Therefore, the functions p(x) and f(x) have the same average rate of change of 1 over the interval [-4, -3]. Thus, the correct answer is: The functions have the same average rate of change of 1.