Can a continuous function have asymptotes?

Answer 1

Yes. It may have horizontal asymptotes, but not vertical asymptotes.

A continuous function may not have vertical asymptotes.

Vertical asymptotes are nonremovable discontinuities. Their existence tells us that there is a value/some values of #x# at which #f(x)# doesn't exist.

However, a continuous function may have horizontal asymptotes.

Consider #f(x)=e^x.# This function is continuous for the set of all real numbers; however, #e^x>=0# for all #x#, IE, there is a horizontal asymptote at #y=0.#

So, horizontal asymptotes don't interfere with the function's continuity.

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Answer 2

Yes, a continuous function can have asymptotes. Asymptotes are lines that a curve approaches but never touches as the independent variable approaches infinity or negative infinity. These asymptotes can occur in functions such as rational functions, exponential functions, and logarithmic functions. However, it's important to note that the existence of asymptotes does not necessarily affect the continuity of a function, as continuity depends on the behavior of the function around its domain.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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