How to find the domain of a log function? (1 Viewer)

[enigma_1]

How do I find other pieces of info enough for me to sketch the graph. Like I know the derivative stuff. But I mean like x--> infinity and stuff.

And the range?

 

[Shadowdude]

Domain of ln(x) is x > 0.

Replace x with whatever.


And range well... depends.

Example question?

 

[hit patel]

Uhh i Think derivative and limits are enough. Although you have to use the domain for inverse and trig functions

 

[enigma_1]

Umm like y=log [(1+x^2)/2]

 

[enigma_1]

How do i use the limit thing? Do I just test values? But it doesn't seem right to do that

 

[panda15]

How do i use the limit thing? Do I just test values? But it doesn't seem right to do that

If you can't find the limits algebraically, then it's perfectly fine to chuck in a really big/small number to see what the limit is.

 

[enigma_1]

But will that get marks in an exam?

 

[Shadowdude]

Well, if you're just graphing it - no.

 

[enigma_1]

Well, if you're just graphing it - no.

So how do you find the features of the graph like the horizontal asymptotes and the limit as x--> infinity, someone please help me lol

 

[HeroicPandas]

Sub in x = positive big number, y will be a big positive number

Then sub in x = negative big number, y will be a big positive number

They are the same because the curve is an even function [f(-x) = f(x)]

Then you want to know what happens at the y-axis right? Then you...?

 

[integral95]

Umm like y=log [(1+x^2)/2]

would be the domain since you can't have a log of a negative

But for all values of x. Therefore the domain would be all real x