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?
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$\begingroup$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.
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