Question

What would be the difference quotient, fx + h fx, for the given function? fx = a, where x is the variable, h is the change in the variable, and a is a constant.

A. 1
B. a
C. x
D. h
E. 0

Answer 1

The difference quotient for the function f(x) = a, where a is a constant, is 0. This is because the change in the output value for any increment h in the variable x is zero, as the function represents a constant value.

Step-by-step explanation:

The student is asking about the difference quotient for a function f(x) = a, where a is a constant. The difference quotient is usually represented as (f(x+h)-f(x))/h. Because f(x) is a constant function, f(x+h) and f(x) will both equal a. So, f(x+h)-f(x) turns into a-a, which simplifies to 0. When you divide 0 by h, you still have 0. The result does not depend on the value of h, so the difference quotient for this function is 0.