graphs of functions?

Question

do the graphs of a square root function and a logarithmic function look the same??

logarithmic: http://oak.cats.ohiou.edu/~piccard/huwe/logarithm.jpg

square root:
http://images.google.com/imgres?imgurl=http://www.richland.edu/james/lecture/m116/functions/sqrt.gif&imgrefurl=http://www.richland.edu/james/lecture/m116/functions/translations.html&h=271&w=278&sz=4&hl=en&start=7&tbnid=27amX2cxsReozM:&tbnh=111&tbnw=114&prev=/images%3Fq%3Dgraph%2Bof%2Bsquare%2Broot%2Bfunction%26gbv%3D2%26svnum%3D10%26hl%3Den%26safe%3Dactive


AND
is the graph of a cube root function practically the same as the graph of a cubic function..only rotated?

cubic:
http://images.google.com/imgres?imgurl=http://jwilson.coe.uga.edu/EMT668/EMT668.Folders.F97/Wynne/Cubic/image3.gif&imgrefurl=http://jwilson.coe.uga.edu/EMT668/EMT668.Folders.F97/Wynne/Cubic/Cubic%2520Functions.html&h=352&w=462&sz=3&hl=en&start=3&tbnid=-53YavWntfdgpM:&tbnh=98&tbnw=128&prev=/images%3Fq%3Dgraph%2Bof%2Bcubic%2Bfunction%26gbv%3D2%26svnum%3D10%26hl%3Den%26safe%3Dactive

cube root:
http://www.math.rutgers.edu/~greenfie/mill_courses/math151/gifstuff/cube_root.gif

AND ONE MORE QUESTION!!

if you were to graph just a parent function of a rational function...arent there multiple possibilities?

Answer 1

The graphs are similar, but not identical.
Try graphing them both on a graphing calculator.

Answer 2

The log function has limit - infinity as x -> 0+, but sqrt has no negative values. Also, sqrt has x-intercept 0 but log has x-intercept x = 1. Finally, while the shapes of the graphs of sqrt and log may appear to be similar, by looking at
lim (x->inf) sqrt(x)/(ln x) we see this limit is +infinity (use L'Hospital's Rule). Therefore the value of sqrt (x) is MUCH LARGER than ln x.

The graph of x^(1/3) is the reflection of x^3 in the line y = x.