Select the correct answer.
Consider function g.
g(x) = 5/x-1 + 2
What is the average rate of change of function g over the interval (-4,3)
A. 2
B. -1/2
C. -7/2
D. 1/2
To find the average rate of change of function g over the interval (-4,3), we need to find the difference in the function values at the two endpoints and divide by the difference in the x-values.
Let's first find the value of g at x = -4:
g(-4) = 5/(-4) - 1 + 2
= -5/4 - 1 + 2
= -5/4 - 4/4 + 8/4
= -1/4 + 8/4
= 7/4
Now, let's find the value of g at x = 3:
g(3) = 5/3 - 1 + 2
= 5/3 - 3/3 + 6/3
= 8/3
Now, we can calculate the average rate of change:
Average rate of change = (g(3) - g(-4))/(3 - (-4))
= (8/3 - 7/4)/(3 + 4)
= (32/12 - 21/12)/7
= 11/12 / 7
= 11/12 * 1/7
= 11/84
Therefore, the correct answer is D. 1/2.
g(x) = 5/(x-1)+2
g(-4) = 5/(-4-1)+2 = 5/-5 + 2 = 1
g(3) = 5/(3-1)+2 = 5/2 + 2 = 9/2
so the average rate of change is
(9/2 - 1)/(3+4) = (7/2)/7 = 1/2