Question

The function is defined for all real values of x. For a constant c, the average rate of change of f(x) from x1 to x2 is given by the expression x2−x1f(x2)−f(x1). Which of the following statements is true?

A) The average rate of change is independent of the constant c.
B) The average rate of change is always negative.
C) The average rate of change is undefined for all values of c.
D) The average rate of change depends on the specific value of c.

Answer 1

The average rate of change depends on the specific value of c.

Step-by-step explanation:

The statement that is true is D) The average rate of change depends on the specific value of c.

The expression x2−x1f(x2)−f(x1) represents the average rate of change of the function f(x) from x1 to x2. The constant c in the function does affect the value of the function, so it will affect the average rate of change. Therefore, the average rate of change depends on the specific value of c.

For example, consider the function f(x) = 2x + c. If we choose x1 = 0, x2 = 1, and c = 1, the average rate of change will be 3. However, if we choose c = 2, the average rate of change will be 4.