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

Dec 6, 2016

x-intercept (y = 0 ) is $- 2$. Asymptotes are horizontal $\leftarrow y = 1 \rightarrow \mathmr{and} v e r t i c a l \uparrow x = 0 \downarrow$. No extrema. No point of inflexion. Graph is inserted.

#### Explanation:

The equation of a hyperbola with asymptotes

$y = {m}_{1} x + {c}_{1} \mathmr{and} y = {m}_{2} x + {c}_{2}$ is

$\left(y - {m}_{1} x - {c}_{1}\right) \left(y - {m}_{2} x - {c}_{2}\right) =$ non-zero constant.

Cross multiplying and reorganizing,

$x \left(y - 1\right) = - 2$. So,

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

As $y \in \left(- \infty , \infty\right)$, sans 1, there are no extrema.

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