Asked by idk the answer
Which statement is true regarding horizontal asymptotes?
A horizontal asymptote cannot be crossed.
Exponential functions don't always have a horizontal asymptote.
Two of these are correct.
None of these are correct.
A horizontal asymptote cannot be crossed.
Exponential functions don't always have a horizontal asymptote.
Two of these are correct.
None of these are correct.
Answers
Answered by
GPT-4o mini
To determine which statement is true regarding horizontal asymptotes, let's analyze each option:
1. **A horizontal asymptote cannot be crossed**: This statement is false. It is possible for a function to cross its horizontal asymptote; horizontal asymptotes describe the behavior of the function as it approaches infinity or negative infinity, but the function can cross this line in finite intervals.
2. **Exponential functions don't always have a horizontal asymptote**: This statement is true. While some exponential functions have a horizontal asymptote (e.g., \(y = e^{-x}\) approaches \(y = 0\) as \(x \to \infty\)), others (e.g., \(y = e^{x}\)) do not have a horizontal asymptote as they grow without bound.
3. **Two of these are correct**: Since we've established that only the second statement is true, this option is false.
4. **None of these are correct**: This option is also false because the second statement is indeed correct.
Therefore, the correct answer is that **Exponential functions don't always have a horizontal asymptote**.
1. **A horizontal asymptote cannot be crossed**: This statement is false. It is possible for a function to cross its horizontal asymptote; horizontal asymptotes describe the behavior of the function as it approaches infinity or negative infinity, but the function can cross this line in finite intervals.
2. **Exponential functions don't always have a horizontal asymptote**: This statement is true. While some exponential functions have a horizontal asymptote (e.g., \(y = e^{-x}\) approaches \(y = 0\) as \(x \to \infty\)), others (e.g., \(y = e^{x}\)) do not have a horizontal asymptote as they grow without bound.
3. **Two of these are correct**: Since we've established that only the second statement is true, this option is false.
4. **None of these are correct**: This option is also false because the second statement is indeed correct.
Therefore, the correct answer is that **Exponential functions don't always have a horizontal asymptote**.
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