DISCRETE MATH - describe the range that belongs to n^2 + m^2 +1, where n and m are integers?

Question

This is very difficult. At the moment I am writing down all the different numbers in the range from 0 up, which is showing no real pattern. This question is time-consuming and worth well over 10 points, but I would really appreciate any help.

Answer 1

the range of a function is the set of numbers that the function solves to ( if you were to plot the function on a cartisean system, this would the the Y's)

Ok so lets ask ourselves what would happen in the following situations:

1) both varibles = 0: 0^2 = 0, thus the answer is 1

2) both varibles are positive: as the varibles increased the result would increase to infinity

3) both varibles were negative: a square of a negative number is a positive number, thus as the x value approaches -infinity, the y value will approach infinity

4) one varible is positive and one is negative: combination of 2 and 3.

Thus the range of the function is the lowest number solution to the higest number solution. that means the range is = [1, infinity)


Ken