Asked by idk the answer
Which statement is true regarding horizontal asymptotes?
Exponential functions don't always have a horizontal asymptote.
A horizontal asymptote cannot be crossed.
Two of these are correct.
None of these are correct.
Exponential functions don't always have a horizontal asymptote.
A horizontal asymptote cannot be crossed.
Two of these are correct.
None of these are correct.
Answers
Answered by
GPT-4o mini
To evaluate the statements regarding horizontal asymptotes:
1. **Exponential functions don't always have a horizontal asymptote.** - This statement is **true**. For example, the exponential function \( f(x) = e^x \) does not have a horizontal asymptote as \( x \) approaches infinity; it increases without bound. However, the function \( g(x) = e^{-x} \) has a horizontal asymptote at \( y = 0 \) as \( x \) approaches infinity.
2. **A horizontal asymptote cannot be crossed.** - This statement is **false**. A horizontal asymptote describes the behavior of a function as \( x \) approaches infinity (or negative infinity). A function can cross its horizontal asymptote at some finite points.
Considering these evaluations:
- The first statement is true.
- The second statement is false.
Thus, the correct answer is **"Exponential functions don't always have a horizontal asymptote."** So the option "Two of these are correct." and "None of these are correct." are not accurate.
Therefore, the answer is **"Exponential functions don't always have a horizontal asymptote."**
1. **Exponential functions don't always have a horizontal asymptote.** - This statement is **true**. For example, the exponential function \( f(x) = e^x \) does not have a horizontal asymptote as \( x \) approaches infinity; it increases without bound. However, the function \( g(x) = e^{-x} \) has a horizontal asymptote at \( y = 0 \) as \( x \) approaches infinity.
2. **A horizontal asymptote cannot be crossed.** - This statement is **false**. A horizontal asymptote describes the behavior of a function as \( x \) approaches infinity (or negative infinity). A function can cross its horizontal asymptote at some finite points.
Considering these evaluations:
- The first statement is true.
- The second statement is false.
Thus, the correct answer is **"Exponential functions don't always have a horizontal asymptote."** So the option "Two of these are correct." and "None of these are correct." are not accurate.
Therefore, the answer is **"Exponential functions don't always have a horizontal asymptote."**
There are no human answers yet. A form for humans to post answers is coming very soon!