how do i get range and domain

Question

y=3⁄x+2

Answer 1

Either way, you find domain and range with the same method.

 

Do you have a graphing calculator?   Or can you get online and find free software (any online graphing calculator can graph this for you)?

 

If the equation is y = (3/x) + 2, you will see a vertical asymptote at x=0 and a horizontal asymptote at y = 2.    You should see a curve in the upper right quarter where these asymptotes cut the graph into 4 quarters.  And another curve in the bottom left quarter.    Notice that the graph never crosses x=0 and it never crosses y=2.   So these are your limitations on x (Domain is all real numbers EXCEPT x=0) and the limitations on y (Range is all real numbers EXCEPT y=2).

 

If the equation is 3/(x+2), then you will see a vertical asymptote at x=-2  and  a horizontal asymptote at y=0.  Should still have two curves, one in the upper right quarter and one in the lower left quarter.  Now your x's are limited to any real number except x=-2  (this is your domain) and your range is only limited by the fact that y never = 0, so the range is all reall numbers EXCEPT for y=0.

 

Wish I could draw the picture of these functions, it makes it so much clearer.  Please do go to an online graphing utility and look at where the graph turns to go straight up and/or turns to go straight down.  The x-value they are avoiding is the vertical asymptote and the limitation on the domain.  Also look for where the graph flattens out.  It will approach the y-value that it appears to flatten to, but will never officially reach it.  This is the y-value that your range must leave out.