Exponential and Logarithmic functions

[Roxy]

How do I find
1. Domain & Range
2. Intervals of increase/decrease
3. max./min values
4. intercepts
5. asymptotes
6. concavity

for Exponential and Logarithmic functions. Can someone explain how I do this in detail pleasezz

These are the types of questions I have (please don't solve them just tell me how to do them:

y= 2x - lnx

y = x^2lnx

y= in(x-1)^2

y = e^x + 1

y= x - lnx

 

[MathStudent]

This is a rather lengthy question, so let's just work on pieces at a time, how about the first equation y = 2x - lnx.
Here are some hints:
- What values of x make this function not meaningful? ( we can exclude these from the domain)
- what can tell us about how a function changes wrt the indepenent variable? (hint it starts with a "d" and ends with "erivative"

That should at least get you going( or thinking in the right direction),,, please show work of any progress and we'll be happy to help you further

 

[Roxy]

This is a rather lengthy question, so let's just work on pieces at a time, how about the first equation y = 2x - lnx.
Here are some hints:
- What values of x make this function not meaningful? ( we can exclude these from the domain)
- what can tell us about how a function changes wrt the indepenent variable? (hint it starts with a "d" and ends with "erivative"

That should at least get you going( or thinking in the right direction),,, please show work of any progress and we'll be happy to help you further

- What values of x make this function not meaningful? ( we can exclude these from the domain)

0 or anything below??

 

[MathStudent]

yes... since the natural log is not defined for any value of x (< or =) to 0

PS
I think this probably would have better gone under homework

 

[Roxy]

I'm confused... with all the explaining.

You can just say stuff like set y' = 0 and stuff like that for all of them.

And thanks for trying to help

 

[digink]

The domain is all the numbers for which you can compute a function on the x-axis. The range is a set of all the numbers that can be computed for the y-axis.

if I am not mistaken the intervals of increase and decrease are seen by just taking the derivative of the function and checking to see if the values are positive or negative.

The asymptotes of the function are easiest found by the limits for which as x->infinity y=a given value which would inturn give you the vertical limit. For the horizontal limit its the limit for which as x->a number the function goes to infinity.

Hope that helps and please clairify me if I've made any mistakes.