What kind of functions have asymptotes?

Functions that exhibit asymptotes are typically rational functions, where the degree of the numerator and denominator determines the presence of vertical and horizontal asymptotes. Additionally, logarithmic functions and certain types of exponential functions can also have asymptotes. Vertical asymptotes occur where the function approaches infinity, while horizontal asymptotes indicate the behavior of the function as it approaches infinity. Overall, asymptotes characterize the end behavior and discontinuities of these functions.