Question

Which of the following is the average rate of change over the interval [-5,10] for the function g(x)=log 2(x+6)-3 ？

a. 4/5
b. 5/4
c. 4/15
d. 15/4

Answer 1

The average rate of change of the function g(x) over the interval [-5,10] is found by calculating g(10) and g(-5), then dividing the difference by the interval width (15). This results in an average rate of change of 4/15. Hence, the correct answer is option (c) 4/15.

Step-by-step explanation:

To find the average rate of change of the function g(x) = log2(x+6) - 3 over the interval [-5,10], we calculate the change in the function values at the endpoints of this interval and divide by the change in x. To do so, we substitute the x values into the given function to acquire the corresponding g(x) values.

First, find g(-5):

• g(-5) = log2(-5+6) - 3 = log2(1) - 3 = 0 - 3 = -3

Next, find g(10):

• g(10) = log2(10+6) - 3 = log2(16) - 3 = 4 - 3 = 1

Now calculate the average rate of change: ARC = [g(10) - g(-5)] / (10 - (-5)) =

(1 - (-3)) / (15) = 4/15

Therefore, the correct option for the average rate of change of the function over the interval [-5,10] is (c) 4/15.