Both the square root and logarithmic functions have a domain limited to x -values greater than 0 . However, the logarithmic function has a vertical asymptote descending towards −∞ as x approaches 0 , whereas the square root reaches a minimum y -value of 0 .

Do logarithmic functions have horizontal asymptotes?

There can't be a horizontal asymptote because no matter how large a y -value you may seek, you can find an x -value that gives you that y . (If you want log2(x+3)=1,000,000 , then you choose x=21,000,000−3. ) Thus, log functions have no maximum (and no horizontal asymptote).

Are there Asymptotes for logarithmic functions?

The graph of a logarithmic function has a vertical asymptote at x = 0. The graph of a logarithmic function will decrease from left to right if 0 < b < 1.