Asymptote/Examples/x^2 + 1 over x

Examples of Asymptotes

Asymptotes to $y = x^2 + \dfrac 1 x$ (blue): $y$-axis (green), and the parabola $y = x^2$ (red)

Consider the curve whose equation in the Cartesian plane is given by:

$y = x^2 + \dfrac 1 x$

This has $2$ asymptotes:

the straight line $x = 0$

the parabola $y = x^2$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): asymptote
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): asymptote