Question

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

f(x) = mx + b where m = 0​

Answer 1

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.

Answer 2

• f(x + 1) – f(x) = m

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.