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In math, I want to say that there is no possibility that an asymptote will be a tangent to the function.

How should I write it?

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    Could you please give us an example sentence with a series of blanks? Because, you see, when you say "asymptote", it already means that a given function will never touch it (horizontal asymptotes can be crossed though). That information is already contained in the word "asymptote". However, you could say something like this: a function gets asymptotically close to a given vertical/horizontal line. – Michael Rybkin Aug 29 '18 at 11:11
  • my study is about horizontal asymptote, the students' error is that they think that vertical and horizontal are equal - can't touch the function. one of their mistakes is that they think the asymptote can intersect the function but can't be a tangent to the function – ascomp Aug 29 '18 at 12:23
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    I'm not sure if I understand what you're saying. An asymptote just can't be tangent to a function at a point because it never touches the graph of the function. The concept of tangency states that the graph of a function and a line to tangent to the function at a particular point only touch each other at that particular point called the point of tangency. Asymptotes and tangent lines are completely different animals. I think you've got everything backwards. – Michael Rybkin Aug 29 '18 at 13:29
  • y=(x^2)/(1+x^4) is tangent to y=0 at (0,0). As x goes to positive or negative infinity, y=0 is an asymptote of y=(x^2)/(1+x^4) I would tell your students that in a range where one function is asymptotically approaching another, the two functions can touch or be parallel, but cannot be tangent to one another. – Adam Aug 29 '18 at 15:09
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I'd say:

The asymptote cannot be a tangent to the function.

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    I would not recommend reposting - you shouldn't post the same question on multiple SE sites. We can migrate the question if it doesn't get a good answer here. – ColleenV Aug 29 '18 at 11:00

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