Dave @ MathNotations posted this nice problem today, good for an Algebra 2 or Precalculus class. I like it:
Consider the following problem:
If -5 ≤ x ≤ 4, and f(x) = 2x2 – 3, how many integer values are possible for f(x)?
For the solution, and some added pedagogical discussion, visit the original post here. Thanks, Dave!
Random Walks 
I approached this problem in a way that is not very elegant but seems to give the correct answer. For f(x) to have an integer value, the 2x^2 term must have an integer value. Over domain [-5, 4], the range of 2x^2 is [0, 50] which contains 51 integer values. So there are 51 integer values possible for f(x).
I think that’s a great way to do it! Absolutely.