Finding the range of a function generally requires graphing, except in the case of horizontal lines. The range refers to all of the possible y-values in a function, which are the dependent values that come from incorporating independent x-values into the equation.
Many times, a math problem provides a function and asks for the domain and the range. With the equation y = 3, the range is the number 3, the graph is a horizontal line crossing the y-axis at 3, and the domain is all real numbers, as the line would extend infinitely in both directions.
Other functions are more complex, though, and require graphing to establish the range. The function y = (x^2 + 10 x + 25)/(x^2 - 1) does not allow all real numbers into the domain, as division by zero doesn't produce a solution. Factoring (x^2 - 1) yields (x+1)(x-1). If x is either 1 or -1, the function involves division by zero, and so the domain is "all x not equal to -1 or 1."
Finding the range in such a situation is fastest through graphing. Drawing a graph of the example function finds that y = 0 when x = -5, but other than that, y > 0. The range for this function, therefore, is "all y greater than or equal to 0."