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
#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
#1 = 1/(x +1)#
#x + 1 = 1#
#x= 0#
Hence,
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!