Graph y=x^(-1/2)

Find where the expression ${\displaystyle \frac{1}{x^{\frac{1}{2}}}}$ is undefined.

Since ${\displaystyle \frac{1}{x^{\frac{1}{2}}}}$${\displaystyle \to }$${\displaystyle \infty }$ as ${\displaystyle x}$${\displaystyle \to }$${\displaystyle 0}$ from the left and ${\displaystyle \frac{1}{x^{\frac{1}{2}}}}$${\displaystyle \to }$${\displaystyle \infty }$ as ${\displaystyle x}$${\displaystyle \to }$${\displaystyle 0}$ from the right, then ${\displaystyle x=0}$ is a vertical asymptote.

Since its numerator approaches a real number while its denominator is unbounded, the fraction ${\displaystyle \frac{1}{x^{\frac{1}{2}}}}$ approaches ${\displaystyle 0}$.

List the horizontal asymptotes:

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes: ${\displaystyle x=0}$

Horizontal Asymptotes: ${\displaystyle y=0}$

No Oblique Asymptotes