Solving for Domain and Asymptotes in Functions f(x) and g(x)

[Heather W]

Please Help with Domain...

Homework Statement

For f(x) Determine Domain, Vertical Asymptote and x and y intercepts. then State and graph the effect of the modifications and sketch the graph of f(x)
Given f(x) = - log3(x – 1) + 2


For g(x) determine domain, Horizontal asymptote and x and y intercepts. then state and graph the effect of the modifications and sketch the graph of g(x)
Given g(x) = 3 - x + 1 - 9

 

[hotcommodity]

Lets begin with the first problem. To find the domain, consider when the log of something not exist. Let me know if this is what's confusing you.

 

[Heather W]

yes that is a confusing part, I know how to find the Domain, but not when involving log

 

[hotcommodity]

Ok, so let's say I have y = log( 2 - x) - 1, and I want to find the domain of the function. You should know that the log of zero, or any negative quantity does not exist. So I would set the function inside of the log equal to zero:

2 - x = 0 ---> x = 2.

Now I know that the function exists as long as x is greater than 2. It does not exist when x is two or less. This is our domain. Does that make sense?

 

[Heather W]

yes thank you.