Question

What would be the difference quotient, [ f (x + h) - f (x) ] ÷ h , for the given function? (f(x) = a, where x is the variable, h is the change in the variable, and a is a constant.

a. 1/h
b. a/h
c. h/a
d. a

Answer 1

The difference quotient for the given function f(x) = a is (b) a/h.

Therefore the correct choice is (b) a/h.

Step-by-step explanation:

The difference quotient is a measure of the average rate of change of a function over a small interval. For the function f(x) = a where a is a constant the difference quotient [f(x + h) - f(x)] / h simplifies to [(a - a) / h] resulting in 0/h which is 0. Therefore the correct choice is (b) a/h.

In this case as the function is a constant a there is no change in the function over the interval (x, x + h) leading to a difference quotient of 0. This aligns with the algebraic simplification of the expression.

Understanding the difference quotient provides insights into the concept of average rate of change in calculus. It is a fundamental concept used in the study of derivatives and helps in analyzing the behavior of functions as the input changes.

Therefore the correct choice is (b) a/h.