What name should I give curves with only one Y value for every X value?

Question

I am writing a software library for general 3D graphics and simulation. I have a strong computer science background, but haven't studied maths since school.

Arbitrary parametric curves are commonly used to animate variables over time. However, such techniques require that curves never 'double back'. If there are multiple solutions for Y at time X, the concept breaks!

Diagram depicting invalid curve due to 'doubled back' region

I plan to write a verification function, which can assert whether a set of 2D points (and an associated interpolation method) would produce a valid animation curve. This could be used for writing tests, or even as a stepping stone to automatically fixing user-provided curves.

Currently such function is named and documented as 'is_valid_animation_curve', but I feel like there would be an existing name for such class of curves. I prefer to use correct technical terminology whenever possible, but I'm out of my depth here!

Answer 1

Putting on my software hat, I would think that is_valid_animation_curve( ) might check other properties.

For the particular property you're asking about here, I might call the validating function is_curve_function_like( ). "Function-like" isn't really a well known or used phrase, but "there's only one $ y $ for each $x$" is the key property for a relation between $x$ and $y $ to be a function, so I'd expect people to understand the name pretty easily. Or maybe is_curve_a_function( ) - it depends on how 'chatty' you like your function names.