Question

Find and simplify the difference quotient f(x + 1) – f(x) for the following function.

Answer 1

Answer:

• f(x + 1) – f(x) = m

Step-by-step explanation:

Let's ignore the fact that m = 0.

The difference is:

• f(x + 1) - f(x) =
• m(x + 1) + b - mx - b =
• mx + m - mx =
• m

So the difference is m, whatever it's value is.

Answer 2

In your situation you said that

• $f(x) = mx+b$
• $m=0$

Putting those together, you'd have $f(x) = b$ because $0\cdot x+b=b$.

To evaluate the difference quotient, first find each piece on it's own:

• $f(x+1) = b$ because $f(x) = b$ no matter what your x-value is.
• $f(x) = b$

So putting those together:

     $f(x+1) - f(x) = b-b = 0$

Remember that the difference quotient is basically finding the slope of something.  Since you were given that the slope is 0, the difference quotient should work out to match that.