What is the term for a line that doesn't touch a function?

Question

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.

I really doubt that it has a name. It doesn't feel useful or significant enough. There may be some archaic term somewhere though. — Arthur, Aug 20 '18 at 13:48
I thought that before too, but I came across its name a while ago but have since forgotten it. I'm fairly sure it does have a name. — Kantura, Aug 20 '18 at 13:50

score 2 · Answer 1 · answered Aug 20 '18 at 13:55

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I don't know if the direct translation gives the correct answer but here in Italy we say that the line is external. Direct translation also can give: outside line, but it doesn't sound very good!

answered Aug 20 '18 at 13:55

Davide Morgante

3,578

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Or in Germany we say Secante, Tangente or Passante. – Dr. Sonnhard Graubner Aug 20 '18 at 14:02
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Italy is practically the same: Secante, Tangente, Esterna! – Davide Morgante Aug 20 '18 at 14:02
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(Comment because this is non worth a separate answer) Translating from the French would give : a non-secant line. – Evargalo Aug 20 '18 at 14:03
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I think it comes from the Latin language, – Dr. Sonnhard Graubner Aug 20 '18 at 14:03
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That is nice that we use the same words. – Dr. Sonnhard Graubner Aug 20 '18 at 14:05
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@Dr.SonnhardGraubner I was thinking the same! Surly they are from latin, from when I studied latin I can recall that Tangente comes from the latin word tangens-entis which means "to touch" and Secante from secare which means "to cut" – Davide Morgante Aug 20 '18 at 14:10
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Yes this is true,nice, Latin language is very importend – Dr. Sonnhard Graubner Aug 20 '18 at 14:13

What is the term for a line that doesn't touch a function?

1 Answers1