Question

Using complete sentences, explain the similarities and differences between the graphs of a radical function and a logarithmic function.

Answer 1

Similarities:
Both concave down.
Both increasing to infinity (no horizontal asymptote or upper bound).
Both have bounded domain (below).

Differences:
Radical has bounded range, Logarithm has unbounded range.
Radical has no asymptote, Logarithm has a vertical asymptote
Radical has closed domain (endpoint included), logarithm has open domain (endpoint excluded)
Radical (square root) is always larger than (natural) logarithm, for large values, much larger.

*this is from yahoo