Question

explain the characteristics and parts of a logarithmic function and its graph.

Answer 1

sorry that's inversely exponentially over my head

Answer 2

LOL.

Answer 3

that's Alg2 man.

Answer 4

Well, let's see. The domain of ln is (0,infinity) and has a range of the entire real line; it's strictly increasing; has one root at x = 1; has a vertical asymptote as x->0+ of the negative y axis. What else?

Answer 5

It has negative second derivative everywhere which means that while it is increasing, it increases at a slowing rate.

Answer 6

Q2:
explain the similarities and differences between the graphs of a radical function and a logarithmic function. 

Answer 7

f(x) = 1/x would be a radical function, for instance?

Answer 8

no it wont be.

Answer 9

what's the definition you are using for a radical function?

Answer 10

the one with radicals. LOL.

Answer 11

\[f(x) = \sqrt{x} -2\]Something like that.

Answer 12

I see. Well, often radical function also have restricted domains like the ln function; i.e., not the whole real line.

O

Answer 13

Often radical functions also have second derivative of just one sign and first derivative also of one sign.

But without a sharper definition of a radical function I'm finding it hard to characterize this in general.

Answer 14

Log functions also have restrictions.

Answer 15

for example f(x) = sqrt(x) is only defined on [0,infty), almost like the ln function; it is tricly increasing and has negative second derivative everywhere. Has only one root on its domain. But unlike the ln function its range is [0,infty)

Answer 16

that'll probably do.

Answer 17

Alright. thanks.