How do I write the function y=6x-2/2x+2 in graphing form??
also, how do I find it's domai and range and how do I describe the end behavior of this function as |x| increases without bound.
I'm not sure what you mean by graphing form, but for the end behavior, the function forms a horizontal asymptote at y = 3. X has the same power in both the numerator and denominator, and therefore it converges at the ratio of the leading coefficients: 6x/2x = 3. Using L'Hopital's Rule from calculus also shows the limit as |x| goes to infinity to be 6/2 = 3.
The domain excludes any numbers where the function is undefined. In this function, x = -1 would make y = -8/0 which is undefined. To find this, just set the denominator equal to zero and solve for x.
2x + 2 = 0
2x = -2
x = -1
The function is defined for all other numbers, so the domain is (-infinity, -1)U(-1, infinity).
I can't remember off hand any good way to find the range other than graphing the function.
I hope this helps..
