Question

The average rate of change of g(x) between x = 4 and x = 7 is Which statement must be true?

A. g(7) - g(4) = 5/7
B. (g(7 - 4))/(7 - 4) = 5/6
C. (g(7) - g(4))/(7 - 4) = 5/6
D. (g(7))/(g(4)) = 5/6

Answer 1

The statement that must be true for the average rate of change of the function g(x) between x=4 and x=7 is C. (g(7) - g(4))/(7 - 4) = 5/6, which correctly represents the slope of the secant line between these two points on the function.

Step-by-step explanation:

The student asked about the average rate of change of a function g(x) between two points, x = 4 and x = 7. To find the average rate of change, you subtract the function values at these points and then divide by the difference in the x values, which gives us the formula:

(g(7) - g(4)) / (7 - 4)

Therefore, the statement that must be true is:

C. (g(7) - g(4))/(7 - 4) = 5/6

This formula represents the slope of the secant line that intersects the curve of g(x) at x = 4 and x = 7. Choice C is the correct expression of the average rate of change as it matches the formula for calculating it.

Answer 2

The statement that must be true for the average rate of change of the function g(x) between x=4 and x=7 is C. (g(7) - g(4))/(7 - 4) = 5/6, which correctly represents the slope of the secant line between these two points on the function.

Step-by-step explanation:

The student asked about the average rate of change of a function g(x) between two points, x = 4 and x = 7. To find the average rate of change, you subtract the function values at these points and then divide by the difference in the x values, which gives us the formula:

(g(7) - g(4)) / (7 - 4)

Therefore, the statement that must be true is:

C. (g(7) - g(4))/(7 - 4) = 5/6

This formula represents the slope of the secant line that intersects the curve of g(x) at x = 4 and x = 7. Choice C is the correct expression of the average rate of change as it matches the formula for calculating it.

Answer 3

The statement that must be true for the average rate of change of the function g(x) between x=4 and x=7 is C. (g(7) - g(4))/(7 - 4) = 5/6, which correctly represents the slope of the secant line between these two points on the function.

Step-by-step explanation:

The student asked about the average rate of change of a function g(x) between two points, x = 4 and x = 7. To find the average rate of change, you subtract the function values at these points and then divide by the difference in the x values, which gives us the formula:

(g(7) - g(4)) / (7 - 4)

Therefore, the statement that must be true is:

C. (g(7) - g(4))/(7 - 4) = 5/6

This formula represents the slope of the secant line that intersects the curve of g(x) at x = 4 and x = 7. Choice C is the correct expression of the average rate of change as it matches the formula for calculating it.