I'm asked to find the range of the function :
$ (-x^2 , +1) $
Taking R as a real number which represents a quantity along a line and graphing :
then the range for this function from viewing the graph appears to be :
$ R = (-\infty , +\infty) $
Is there an alternative method of finding the range of this function without using a graph ?
Watching the khan academy tutorial suggests using graphs : https://www.khanacademy.org/math/algebra/algebra-functions/domain-and-range/v/domain-and-range-from-graphs but is there a pure algebraic method instead of using graphs ?
It is not clear what the range is when the range appears infinite as how do we know that at some point on the axis the range functions stops tending towards infinity ?