10. Which of the following are potential horizontal asymptotes for exponential functions? a. \( y=-1 \) b. \( y=0 \) c. \( y=1 \) d. None of the available answers

Exponential functions generally have a horizontal asymptote, which is determined by their behavior as \( x \) approaches infinity or negative infinity. For example, the function \( f(x) = e^x \) approaches \( y=0 \) as \( x \rightarrow -\infty \), indicating that \( y=0 \) is a horizontal asymptote. Meanwhile, exponential functions do not approach non-zero constants like \( y=1 \) or \( y=-1 \) when evaluating their limits at extremes. In practice, recognizing horizontal asymptotes can help in graphing the behavior of exponential functions. Since these functions grow rapidly, understanding their asymptotic behavior provides valuable insights for fields like population modeling, finance (e.g., compound interest), and natural processes, ensuring accurate predictions in various real-world scenarios.