How do you graph #y=(3x^2)/(x^2-9)# using asymptotes, intercepts, end behavior?

1 Answer
Nov 23, 2016

Answer:

Horizontal asymptote: y = 0 and vertical ones are #x =+-3#. In #Q_1, # as #x to oo, y to 0 and# as #y to oo, x to 0#. See explanation, for continuation on end behavior.

Explanation:

graph{y(x^2-9)-3x^2=0 [-40, 40, -20, 20]}

By actual division and rearrangement,

#(y-3)(x-3)(x+3)=27#

To get asymptotes, See that, #LHS to 0 X (+-oo)# indeterminate

form, so that the limit exists as 27.

Easily, you could sort ouy the equations to the ayymptotes by setting

the factors on the LHS to 0.

Answer:

Horizontal asymptote is y = 0 and the vertical ones are #x=+-3#.

In #Q_1, # as #x to oo, y to 0 and# as #y to oo, x to 0#.

In #Q_2#, as #x to -oo, y to 0 and# as #y to oo, x to 0#.
.

In #Q_3 and Q_4#, as #x to 0# , as # y to -oo#