Parallel AsymptotesBy definition, any lines that are not parallel will intersect eventually. But to be...

Haley Madden

Haley Madden

Answered

2022-07-21

Parallel Asymptotes
By definition, any lines that are not parallel will intersect eventually. But to be parallel lines, both lines must have the same slope. However, consider this situation:
There is a exponential graph that is an asymptote on the y-axis and on the same graph there is a reflection across the y-axis of the first exponential curve.
Now, we know that since these lines are asymptotes they will never actually reach the y-axis (where they would intersect). But also, they do not have the same slope. So - my question is - are these lines parallel?

Answer & Explanation

le1kabp

le1kabp

Expert

2022-07-22Added 11 answers

Your definition that says "lines that never meet are parallel" is using "line" is a different way than you are. That definition is referring to a straight line in a 2-D Euclidean geometry, which the graph of your function is not.
To avoid this confusion, the graph of a function is often called a "curve" and only called a "line" when it happens to be straight.

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