Are hyperbolas not functions?

Question

Explain in terms of conic sections how hyperbolas are not functions.

Is it because the vertical line intersects both sides of the conic section, making it so that each of the two hyperbolas fails the vertical line test?

Answer 1

I guess you're asking about the graph of a function. But the graph of a function can be a hyperbola. Example: $f: \mathbb{R}-\{0\} \to \mathbb{R} - \{0\}$, $f(x) = \frac{1}{x}$

Answer 2

The premise isn't true: almost all the functions of the form

$$ f(x) = \frac{ax^2 + bx + c}{dx + e} $$

Where $ ax^2 + bx + c \neq 0,\ $ and $\ d \neq 0 $ have a hyperbola as graph.

You cannot represent as a function a hyperbola with the two asintotes oblique lines: one of them has to be a vertical line.