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
B. ( a )
C. ( x )
D. ( h )
E. 0

Answer 1

The difference quotient for the function f(x) = a is zero, because the function's value does not depend on x and thus remains constant even as x changes.

Step-by-step explanation:

The difference quotient (f(x + h) - f(x)) / h is used to find the average rate of change of a function over the interval from x to x + h. For the given function f(x) = a, where a is a constant, both f(x) and f(x + h) will equal a since the function's value does not depend on x. Therefore, the difference quotient simplifies as follows:

f(x + h) - f(x) = a - a = 0

And then, divide by h:

0 / h = 0

Since any number divided by h (where h is not zero) will be 0 if the numerator is 0, the difference quotient for the function is 0.