The function f(x) has the property that if P and Q are any two distinct points on the graph of y = f (x), then the slope of PQ is equal to 1. What is the value of f(10) - f(0)?
\(\phantom{twice the sum of the x-coordinates of P and Q.}\)
+289 Make sure you credit where the original problem came from! This, I believe, is from MATHCOUNTS States.
In the graph of y = f(x), we know that two coordinates are:
(10, f(10))
(0, f(0)).
Finding the slope of these two points gives us:
(f(10)-f(0))/10 = 1
Therefore, f(10)-f(0) = 10.
