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QUESTION

# How do you find the slant asymptote of f(x) =( x^2 + 3x - 3) / (x+4)?

Slant asymptote: y = x-1. See the -inclusive graph.

By division,

y = f(x)= x-1+1/(x+4)

Rearranged,

(y-x+1)(x+4)=1, revealing that the graph is a hyperbola with

asymptotes

(y-x+1)(x+4)=0.

Separately,

y-x+1=0 gives a slant asymptote and

x+4=0 gives a vertical asymptote.

graph{((y-x+1)(x+4)-1)(y-x+1)(x+0.000001y+4)=0 [-23, 23.02, -12.7, 12.6]}