Question

how do i solve and sketch y=x-1/x+1

Answer 1

well, for starters vertical asymptote at x = -1

Answer 2

This looks like a hyperbola

Answer 3

whats the limit of y as x -> infinity and -infinity?

Answer 4

hmm, perhaps you need to divide top and bottom by the highest power of x (in this case x)

Answer 5

y = (1-1/x)/(1+1/x)

Answer 6

so when x -> infinity, y = (1-[0])/(1+[0]) = 1
when x -> -infinity, y = (1-[0])/(1+[0]) = 1

Answer 7

Can you graph it now?

Answer 8

sorry went away for a moment ill just take a look at the answer

Answer 9

i was thinking along the lines of y = 0-1/0+1=-1, and when solving the equation x-1/x+1 i solved in the form (x-1)/(x+1)(x+1)^2 = (x-1) (x+1) x=1 & x=-1 but whether x approaches from above the x axis or below i'm not sure

Answer 10

the denominator is 0 at x = -1 therfore the domain is the set of all real numbers eccept for -1
as x approaches -1 from the left infinity proceeds in the negative direction

Answer 11

approaching from the right infinity proceeds ion the positive direction, but from above or below the x axis

Answer 12

if you can sketch it it would be much easier

Answer 13

ok i worked it out now for the next one