Compare the average rates of change for the graphed square root function p (x) = Square root of x + 4 and the cube root function f (x) = ^3square root of x + 4 over the interval [-4, -3].
A. The functions have the same average rate of change of 1.
B. The functions have the same average rate of change of 0.
C. The square root function has the greater average rate of change.
D. The cube root function has the greater average rate of change.
To find the average rate of change of a function over an interval, we need to calculate the change in the function's values divided by the change in the input values.
For the square root function p(x) = √(x+4), the average rate of change over the interval [-4, -3] is given by:
(√(-3+4) - √(-4+4)) / (-3 - (-4))
= (√1 - √0) / (-3 + 4)
= 1 / 1
= 1.
For the cube root function f(x) = ∛(x+4), the average rate of change over the interval [-4, -3] is given by:
(∛(-3+4) - ∛(-4+4)) / (-3 - (-4))
= (∛1 - ∛0) / (-3 + 4)
= 1 / 1
= 1.
Therefore, the average rates of change for both the square root function and the cube root function over the interval [-4, -3] are the same, which is 1.
So, the correct answer is:
A. The functions have the same average rate of change of 1.