Expert: Josh - 10/16/2008

Question
How do you find range for any equation? I forgot how to and none of the sites help me understand how to find range in an function.

Answer
Hi Trace,

The range is the set of all possible values that a function can take.
Consider the equation y=(x-2)^2 +1 for a parabola. As you can see, the (x-2)^2 part attains a minimum of zero. This added to 1 gives a minimum value of 1 for the equation y. The axis of symmetry is given by x=2. As x moves away (on either side) from x=2, the (x-2)^2 part can only increase. In fact it increases in an unbounded manner. i.e., as x goes to infinity, (x-2)^2 also goes to infinity in the limit and y must follow as well.

So, to summarize, this function y can take any value between 1 (including one itself) and infinity. So, the range is [1,inf). If you are still unsure, just tabulate the values of x versus y.
...
x=100, y=?
x=8, y=?
x=4, y=?
x=2.01, y=?
x=2, y=?
x=1.99, y=?
x=-2, y=?
x=-6, y=?
x=-98, y=?
and so forth to see what happens

You need to get a good textbook and practice doing many questions before you can get the hang of this. But the general principle is to find the set of all possible values that a function can take to work out the range.