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

1 Answer
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]}