Math Is Fun Forum

surajaz

Member

Registered: 2008-08-01

Posts: 0

function

1. Find the range of function Y=x/1+x

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: function

Personally, I'd divide the fraction out to give y = 1 - 1/(x+1)

This should be relatively easy to draw - the curve 1/x is shifted one unit to the left, reflected across the x-axis, and then shifted one unit up. Once you've drawn it you should be able to state the range.

gnitsuk

Member

Registered: 2006-02-09

Posts: 121

Re: function

Well, strictly, to determine the range, we need to know the domain.

I'll assume that the domain is all real values of x.

Then we can easily see from the function (especially in the form suggested by Daniel123):

that the function can take on ALL real values of y other than y = 1. This is because for EVERY value of x (except x = -1) y will have a value. When the magnitude of x tends to large values, so y will be nearly 1 because then:

For other values of x, obviously 1/(x+1) can go through any value.

Moreover, the range of the function is:

Plot of  y = x / (x+1)

Last edited by gnitsuk (2008-08-22 02:07:31)