Mrs.Rivenell says that the average rate of change between x = -6 and x = -3 for the function; f(x) = (3x-2)(x+5) / x^2+6x+5 is 0.5.
Mr. Blakely, disagrees. With whom do you side and why?
It helps to note that f(x) = (3x-2)/(x+1)
but f(-5) is undefined.
Luckily, it's just a point discontinuity, not an asymptote.
So, the average rate of change is
(f(-3)-f(-6))/(-3-(-6)) = (11/2 - 4)/3 = 1/2
no idea which documents you searched ...
To determine if Mrs. Rivenell or Mr. Blakely is correct, we need to calculate the average rate of change for the given function between x = -6 and x = -3 and compare it to the value of 0.5.
The average rate of change of a function f(x) over the interval [a, b] is given by the formula:
Average Rate of Change = [f(b) - f(a)] / (b - a)
Let's calculate the average rate of change for the given function between x = -6 and x = -3 and see if it is equal to 0.5.
First, calculate f(-6) and f(-3):
f(-6) = [(3 * -6 - 2) * (-6 + 5)] / (-6^2 + 6 * -6 + 5)
= (-20 * -1) / (36 - 36 + 5)
= 20 / 5
= 4
f(-3) = [(3 * -3 - 2) * (-3 + 5)] / (-3^2 + 6 * -3 + 5)
= (-11 * 2) / (9 - 18 + 5)
= -22 / -4
= 11 / 2
= 5.5
Now substitute these values into the average rate of change formula:
Average Rate of Change = (f(-3) - f(-6)) / (-3 - (-6))
= (5.5 - 4) / (-3 + 6)
= 1.5 / 3
= 0.5
Based on the calculations, we can conclude that the average rate of change between x = -6 and x = -3 for the given function is indeed 0.5. Therefore, I side with Mrs. Rivenell and agree that the average rate of change is 0.5.
To verify who is correct, we need to calculate the average rate of change between x = -6 and x = -3 for the given function. The average rate of change is determined by finding the difference in the function values at the two points and dividing it by the difference in the x-values.
First, let's find the function values at x = -6 and x = -3:
For x = -6:
f(-6) = (3(-6)-2)(-6+5) / (-6)^2+6(-6)+5
= (-20)(-1) / 36-36+5
= 20 / 5
= 4
For x = -3:
f(-3) = (3(-3)-2)(-3+5) / (-3)^2+6(-3)+5
= (-11)(2) / 9-18+5
= -22 / -4
= 5.5
Now, let's calculate the average rate of change:
Average rate of change = (f(-3) - f(-6)) / (-3 - (-6))
= (5.5 - 4) / (-3 + 6)
= 1.5 / 3
= 0.5
From the calculation, we can see that the average rate of change is indeed 0.5. Therefore, Mrs. Rivenell is correct in stating that the average rate of change between x = -6 and x = -3 for the given function is 0.5.