How do you graph #y=-5/x# using asymptotes, intercepts, end behavior?

1 Answer
Jul 9, 2018

Answer:

See answer below

Explanation:

Given: #y = -5/x#

This is called a rational function: #(N(x))/(D(x))#.

Find vertical asymptote(s):

When #D(x) = 0# we have vertical asymptotes:

vertical asymptote at #x = 0#

End conditions:
The negative coefficient means the graph is reflected about the #x#-axis. So instead of starting in above the #x#-axis, the function starts below the #x#-axis.

Find y-intercept by setting #x = 0:#

#y = -5/0 => y = #undefined. #" no "y#-intercept

Find x-intercepts by setting #y = 0: " "0 = -5/x#

Multiply both sides by #x: " "0 * x = -5, " "0 = -5 # Not TRUE

This means there is no #x#-intercepts.

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