Question

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

Answer 1

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]}