sketch the curve y=x/x-1?

Question

find max/min and others

Answer 1

y' = [(x-1) - x] / (x-1)^2 = -1/(x-1)^2, so no critical points. y' < 0 for all x where y is defined, so it's always decreasing.

y'' = 2/(x-1)^3, which is positive when x>1, and negative for x<1. Therefore the curve is concave up for x>1, and concave down when x<1.

There is a vertical asymptote at x=1, and lim x->inf x/(x-1) =
lim x->inf 1/(1-1/x) = 1 (same for x -> -inf) so there is a horizontal asymptote at y=1.

Answer 2

First you have to find the verical asymptote. which is found by setting (x-1) =0. For the horizontal asymptote you use limit of x/(x-1) as x approches 0 which equal to 1.
If you're still not sure how it looks like you can do a table on both sides to see what it will look like.

It looks like a slanted hyperbola.

Answer 3

maximum = infinity
minimum = minus infinity

The max/min is x = 1
the curve slopes down and to the right on the RHS of (x = 1)
the curve slopes up and to the left of the LHS of (x = 1)

Answer 4

6 Sep 2008 ... ( a, f ( a ) ) is a table certain area of inflexion. ... Eg 2. 2008 J1 term examination Q10 A curve has parametric equations x ... y= x 2 + ax + 4 . x+b x = ?a million and a table certain element at ... [4] Draw a comedian strip of C, exhibiting of course any axial intercepts, asymptotes and table certain factors. ...

Answer 5

Domain: 1< positive infinity
1> negitive infinity

Range: 1< positive infinity
1> negitive infinity

max=pos infinity
min=neg infinity
(x,1) cannot be the graph approaches 1, but will never reach it
(1,x) can not be the graph approaches 1, but will never reach it

Could give you the graph, but you don't recieve email.