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

  • Thread starter Heather W
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In summary, the conversation discusses finding the domain, vertical and horizontal asymptotes, and x and y intercepts for two functions and graphing the effects of modifications. The first function is f(x)=-log3(x-1)+2 and the second function is g(x)=3-x+1-9. The concept of the log of a negative or zero quantity not existing is also explained to find the domain.
  • #1
Heather W
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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
 
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  • #2
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.
 
  • #3
yes that is a confusing part, I know how to find the Domain, but not when involving log
 
  • #4
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?
 
  • #5
yes thank you.
 

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

What is a domain in a function?

A domain in a function refers to the set of all possible input values for the independent variable (usually denoted as x). It is the range of values for which the function is defined and can produce an output.

How do you determine the domain of a function?

To determine the domain of a function, you need to look for any restrictions on the independent variable. This can include values that would result in a division by zero, negative values under a square root, or values that would make the function undefined. Once you have identified these restrictions, you can determine the range of input values that are allowed for the function.

What are asymptotes in a function?

An asymptote in a function is a line that a graph approaches but never touches. It can be a horizontal, vertical, or oblique line that represents the behavior of the function as the input values approach certain values. Asymptotes are important in understanding the behavior of a function and can help determine its domain.

How do you find asymptotes in a function?

To find asymptotes in a function, you need to analyze the behavior of the function as the input values get larger or smaller. For horizontal asymptotes, you need to look at the end behavior of the function. For vertical or oblique asymptotes, you need to check for any restrictions on the input values that would cause the function to approach infinity or be undefined.

Why is it important to solve for domain and asymptotes in functions?

Solving for domain and asymptotes is important because it helps us understand the behavior of a function and identify any potential issues or restrictions. It also allows us to accurately graph the function and make predictions about its outputs. Additionally, finding the domain and asymptotes can help us solve real-world problems that involve functions and their inputs.

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