How do you graph #(-2x^2)/(3x+6)# using asymptotes, intercepts, end behavior?

1 Answer
A. S. Adikesavan
Jan 17, 2017

Slant asymptote: #2x+y-4=0# Vertical asymptote { #uarr x = -2 darr#
. The asymptotes design proximity ( getting the graph closer ), as the end behavior. x-intercept:#2sqrt2. y-intercept: 8.

Explanation:

By actual division,

it is #y = -2x+4-8/(x+2)#, giving the form

#(y+2x-4)(x+2)=8# that represents a hyperbola having

#(y+2x-4)(x+2)=0# as asymptotes,

meeting at the center #C(-2, 8)#.

The asymptotes design proximity ( getting the graph closer ), as the

end behavior.

See the asymptotes-inclusive Socratic graph.

x-intercept ( y = 0 ) :#2sqrt2.

y-intercept ( x = 0 ) : 8 : 8

graph{((y+2x-4)(x+2)-8)((y+2x-4)(x+2+.0001y))=0 [-20, 40, -10, 20.]}

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