MHB What Determines the Range of a Rational Function Like f(x) = 2/(x - 3)?

AI Thread Summary
The discussion focuses on determining the range of the rational function f(x) = 2/(x - 3). The range is defined as all the values the function can assume over its domain. Participants explore methods for finding the range, including graphing and analyzing the function's behavior near critical points, specifically the values 3 and 0. There is some confusion regarding the relationship between the domain of the inverse function and the range of the original function. Overall, the conversation emphasizes the importance of understanding the function's characteristics to accurately determine its range.
mathdad
Messages
1,280
Reaction score
0
Find the range of
f(x) = 2/(x - 3).

1. What exactly are we looking for when we say RANGE of a rational function?

2. Is the domain of the inverse the range of the given function?

3. What is the easiest way to find the range? Graphing?
 
Mathematics news on Phys.org
1. All the values a function assumes over its domain.

2. Let's see:

y = 2/(x - 3)

x - 3 = 2/y

x = 2/y + 3

y^(-1) = 2/x + 3

What conclusions may we draw? (look at the values 3 and 0 in both functions).

3. Depends on the function (in my opinion).
 
greg1313 said:
1. All the values a function assumes over its domain.

2. Let's see:

y = 2/(x - 3)

x - 3 = 2/y

x = 2/y + 3

y^(-1) = 2/x + 3

What conclusions may we draw? (look at the values 3 and 0 in both functions).

3. Depends on the function (in my opinion).

I do not understand your answer to question 1.
I also do know what conclusions we can draw based on the values of 3 and 0 in both functions.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Replies
1
Views
1K
Replies
9
Views
2K
Replies
6
Views
2K
Replies
4
Views
3K
Replies
9
Views
2K
Back
Top