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

1 Answer
Jun 10, 2018

See graph

no holes.

Explanation:

Set x=0x=0 to solve for yy intercept:

f(x)=-3/xf(x)=3x

-3/030 in undefined so no yy intercept exists

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

0=-3/x0=3x

0=-30=3 is not possible so no xx intercept(s) exist.

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

Set the denominator=0 to solve fo asymptotes:

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

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

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