Exponential and Logarithmic functions

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Discussion Overview

The discussion revolves around how to analyze exponential and logarithmic functions, specifically focusing on determining their domain, range, intervals of increase and decrease, maximum and minimum values, intercepts, asymptotes, and concavity. Participants are seeking detailed explanations and methodologies for these analyses without direct solutions to specific problems.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant asks for guidance on how to find the domain and range, intervals of increase/decrease, maximum/minimum values, intercepts, asymptotes, and concavity for various exponential and logarithmic functions.
  • Another participant suggests starting with the first function, y = 2x - lnx, and hints at considering the values of x that make the function not meaningful to determine the domain.
  • There is a reiteration of the importance of derivatives in understanding how a function changes with respect to the independent variable.
  • A participant confirms that the natural logarithm is not defined for x values less than or equal to 0, which affects the domain of the functions discussed.
  • One participant expresses confusion about the explanations provided and suggests that simpler statements, such as setting the derivative equal to zero, would suffice.
  • Another participant offers a brief overview of how to determine the domain, range, intervals of increase and decrease, and asymptotes, while inviting clarification on any potential mistakes in their explanation.

Areas of Agreement / Disagreement

Participants generally agree on the importance of understanding the domain and the role of derivatives in analyzing functions. However, there is some disagreement regarding the level of detail and complexity in the explanations, with some participants preferring more straightforward guidance.

Contextual Notes

Some assumptions about the functions, such as the behavior of logarithmic functions at certain values, are discussed but not fully resolved. The discussion also reflects varying levels of comfort with mathematical terminology and concepts among participants.

Roxy
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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
 
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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 :-p
 
MathStudent said:
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 :-p

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

0 or anything below??
 
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 :rolleyes:
 
Last edited:
I'm confused... :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
 
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.
 

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