Expert: Josh - 4/12/2005

Question
what does range mean?...like in something like this (2,1) i know the domain is the 2 but what is range

Answer
(2,1) represents one coordinate in the X-Y plane.

We identify x=2 as the abscissa (also called, x-value) and y=1 as the y-value.

Suppose that we are talking about a straight-line equation of the form y=0.5*x. You can see that the point lies on this line. We see that it satisfies the equation, simply by putting x=2 into y=0.5*x and we obtain y=1, which is consistent with the point (2,1).

The word "range" actually refers to what possible range of y values you can obtain from such a function, given an input x. It doesn't make sense to talk about a single point. Rather, we are interested in the set of all possible points that lie on this equation.

For y=0.5*x, x can take any value from -infinity to +infinity. So, we say that the domain is -inf<x<inf.

Similarly, y here can take any value from -infinity to +infinity. So, the range is -inf<y<inf.

Consider the equation for a circle x^2+y^2=4. Here, the interpretation is that the radius is "sqrt(4)=2".
Both the domain (i.e., x) and range (i.e., y) are restricted to the interval -2<=x<=2 and -2<=y<=2 respectively.

If we shift the circle vertically by 1 unit. The equation, x^2+(y-1)^2=4, for instance can only take input x in the domain -2<=x<=2. But the range y is between -1 and 3.

Draw a graph to see this.