How do you find intercepts, extrema, points of inflections, asymptotes and graph y=(x+2)/x?

1 Answer
A. S. Adikesavan
Dec 6, 2016

x-intercept (y = 0 ) is -2. Asymptotes are horizontal larr y =1 rarr and vertical uarr x = 0 darr. No extrema. No point of inflexion. Graph is inserted.

Explanation:

The equation of a hyperbola with asymptotes

y= m_1x+c_1 and y = m_2x+c_2 is

(y-m_1x-c_1)(y-m_2x-c_2)= non-zero constant.

Cross multiplying and reorganizing,

x(y-1)=-2. So,

the asymptotes are x = 0 and y =1 1 that are at right angles.

As y in (-oo, oo), sans 1, there are no extrema.

y''=4/x^3 that cannot become 0. So, there is no point of inflexion.
graph{x(y-1)-2=0 [-10, 10, -5, 5]}

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