Question

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

Answer 1

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.]}