How do you sketch the graph of f(x)=(x+1)^(-1)???

1 Answer
May 18, 2017

This is equivalent to saying

f(x) = 1/(x + 1)

This is a rational function that will have vertical asymptotes at x= -1. Now we must derive the equation of the horizontal asymptote.

y = lim_(x->oo) (1/x)/(x/x + 1/x)

y = lim_(x->oo) (1/x)/(1 + 1/x)

y = (lim_(x->oo) 1/x)/(lim_(x->oo) 1 + lim_(x->oo) 1/x)

y= 0/(1 + 0)

y= 0

Therefore, there will be a horizontal asymptote at y= 0. Now find the invariant points. These will occur at y = +-1.

1 = 1/(x +1)

x + 1 = 1

x= 0

Hence, (0, 1) will also serve as a y-intercept.

AND

-1 = 1/(x + 1)

-1(x + 1) = 1

-x - 1 = 1

-x = 2

x= -2

So, the graph resembles the following:

graph{y = 1/(x + 1) [-10, 10, -5, 5]}

Hopefully this helps!