Is the graph of the $\frac{1}{x^2}$ function a horizontal hyperbola?

Question

Is the graph of the $\frac{1}{x^2}$ function a horizontal hyperbola? What type of function is this function? Is it a power function or a rational function?

Answer 1

A power function is in the form of $$y=ax^n$$ In your case, $n = -2$, $a=1$.

A rational function is a fraction where both the numerator and the denominator are polynomials.

Since both $1$ and $x^2$ are polynomials, $\frac{1}{x^2}$ is a rational function.

Hyperbola is in the form of $$\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1,$$ so $\frac{1}{x^2}$ is not a hyperbola.

In conclusion, $\frac{1}{x^2}$ is both a rational functional and a power function, but not a hyperbola.

Edit: $\frac{1}{x^2}$ is not a conic section, so it should not be considered as a hyperbola.