Range of Rational Function (No Graphing)

mathdad

mathdad

Full Member
Joined
Apr 24, 2015
Messages
925
How do we find the range of rational functions involving radicals without graphing the functions?

Sample

Find the range of f(x).

f(x) = [sqrt{9 - x^2}]/[sqrt{4 - x^2}]
 
mathdad said:
How do we find the range of rational functions involving radicals without graphing the functions?

Sample

Find the range of f(x).

f(x) = [sqrt{9 - x^2}]/[sqrt{4 - x^2}]
Click to expand...
Calculus is a great tool to find the range of a function. Are you allowed to use calculus to solve this problem?

🤔
 
mario99 said:
Calculus is a great tool to find the range of a function. Are you allowed to use calculus to solve this problem?

🤔
Click to expand...
1. Mario is a Spanish name. I hope you are Puerto Rican.

2. I am doing a self-study of math learned back in the 1980s and early 1990s.

3. I never took calculus.

4. Perhaps you can answer the question with a graph to make it easier.
 
mathdad said:
1. Mario is a Spanish name. I hope you are Puerto Rican.
Click to expand...
Unfortunately no.

mathdad said:
2. I am doing a self-study of math learned back in the 1980s and early 1990s.
Click to expand...
You are awesome. I raise my hat for you.

mathdad said:
3. I never took calculus.
Click to expand...
You are missing half the beauty of math without calculus. Please, study it.

mathdad said:
4. Perhaps you can answer the question with a graph to make it easier.
Click to expand...
I can answer the question with graph, without graph. With calculus and without calculus.

But since you have never taken calculus, let us pretend calculus does not exist. We will also pretend that we are in an exam and graph is not allowed.

There are many ways to find the range. My approach starts by first finding the domain. Do you know how to find the domain of this function?

[imath]\displaystyle f(x) = \frac{\sqrt{9 - x^2}}{\sqrt{4 - x^2}}[/imath]
 
mario99 said:
Unfortunately no.


You are awesome. I raise my hat for you.


You are missing half the beauty of math without calculus. Please, study it.


I can answer the question with graph, without graph. With calculus and without calculus.

But since you have never taken calculus, let us pretend calculus does not exist. We will also pretend that we are in an exam and graph is not allowed.

There are many ways to find the range. My approach starts by first finding the domain. Do you know how to find the domain of this function?

[imath]\displaystyle f(x) = \frac{\sqrt{9 - x^2}}{\sqrt{4 - x^2}}[/imath]
Click to expand...
1. Before we proceed, what is your nationality? I am curious about where you are from.

2. I was told that the domain of the inverse of f is the range of the given function. Is this true?

3. I don't know how to find the range. It has been many years.
 
mathdad said:
1. Before we proceed, what is your nationality? I am curious about where you are from.
Click to expand...
This question, I cannot answer it right now.

mathdad said:
2. I was told that the domain of the inverse of f is the range of the given function. Is this true?
Click to expand...
I am not sure if this is true for all functions, but in general yes.

mathdad said:
3. I don't know how to find the range. It has been many years.
Click to expand...
I asked about the domain, not the range. Do you know how to find the domain of the function you have posted in the OP?
 
mario99 said:
This question, I cannot answer it right now.


I am not sure if this is true for all functions, but in general yes.


I asked about the domain, not the range. Do you know how to find the domain of the function you have posted in the OP?
Click to expand...
Why can't you tell me your nationality?
 
mathdad said:
This chat is now over. I've got a feeling that you are a Biden person. I don't text or chat with Biden and his goons.
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And I have a feeling that you are professor Jambo. But professor Jambo is very good in calculus. Now I am confused!

🤨
 
mario99 said:
And I have a feeling that you are professor Jambo. But professor Jambo is very good in calculus. Now I am confused!

🤨
Click to expand...
Since you are very slow, let me spell it out for you. I don't need your math help. Moving on....
 
mathdad said:
Since you are very slow, let me spell it out for you. I don't need your math help. Moving on....
Click to expand...
Ahhh I remember you now. Your as... has been kicked brutally in 2019 and you are still alive. (Very amazing!)

harpazoooooooooooO

I am sure that you don't remember me

😛

And you will never lol

Important Note to the Seniors: This person mathdad whose other account is harpazo is not either a real student nor a serious-learning person. I will not say he is a bad person, but his main purpose in this site (And other sites) just making fun of others, especially Elite Members. If I were you, I would ignore all of his posts.
 
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