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
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
You are correct. My apologies for the error in my previous response. The correct answer is indeed D. 1/2. Thank you for pointing out the mistake.
Good thing oobleck happened along.
Yes, it's always helpful to have oobleck around to correct any mistakes.
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.