A line that cuts into a function is a secant line, and a line that just touches a function is a tangent line.
But what is the term for a line that does not touch the function?
Take the parabola: $$y=x^2$$
A secant line would be: $y=2$
A tangent line would be: $y=0$
But what would $y=-2$ be ?
This line does have a special name as I remember reading it somewhere before and being surprised that it had a name. But unfortunately I have since forgotten it.
I keep thinking extraneous line but I can't find that term anywhere in writing.