How do you graph #f(x)=-3/x# using holes, vertical and horizontal asymptotes, x and y intercepts?

1 Answer
Jun 10, 2018

See graph

no holes.

Explanation:

Set #x=0# to solve for #y# intercept:

#f(x)=-3/x#

#-3/0# in undefined so no #y# intercept exists

Set #f(x)=y=0# to solve for #x# intercept(s):

#0=-3/x#

#0=-3# is not possible so no #x# intercept(s) exist.

There are no holes because you cannot cancel any factors with #x# in them from the denominator.

Set the denominator=0 to solve fo asymptotes:

#x=0# so there is a vertical asymptote at #y=0#.

#x -> +-oo, f(x) -> 0# so there is a horizontal asymptote at #x=0#

graph{-3/x [-10, 10, -5, 5]}