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!