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Mustard
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- Homework Statement
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- Relevant Equations
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Not sure how to go about this. Would relying on a hole or asymptote work?
yes, the function need not be continuous.Mustard said:Homework Statement:: Look at snippet
Relevant Equations:: Look at snippet
View attachment 268806
Not sure how to go about this. Would relying on a hole or asymptote work?
Hmmm... I was thinking of a function like f(x)= 4x-8/x-2 = 4(x-2)/x-2 = 4, that would make a hole at x=2.ehild said:yes, the function need not be continuous.
The function has to be defined at x=2.Mustard said:Hmmm... I was thinking of a function like f(x)= 4x-8/x-2 = 4(x-2)/x-2 = 4, that would make a hole at x=2.
But would also make f(2) = 4 ? Would it be safe to assume since there is a hole at (2,4) , it is undefined therefore f(2) does not equal 4 ?
Do you mean like a piece wise function ?ehild said:The function has to be defined at x=2.
You can define it in a way everywhere except x=2, and define its value separately at x=2.
You need more parentheses.Mustard said:I was thinking of a function like f(x)= 4x-8/x-2 = 4(x-2)/x-2 = 4
ehild said:You can define it in a way everywhere except x=2, and define its value separately at x=2.
Yes.Mustard said:Do you mean like a piece wise function ?
epenguin said:I suppose you can take any function, and define another function as that one multiplied it by (x - 2) and also divided by (x - 2) - I defer to the mathematicians as to whether that is formally a bona fide new function but even if it is it looks to me trivial and cheating.
epenguin said:The problem says that f(2) ≠ 4 but it doesn't say it has to be equal something or be defined. Probably you have studied before functions which at some point become equal to 0/0 but you were able to find their limit at that point? So you could adapt one of those, I guess that is what the question is expecting.
A function is a mathematical relationship between two sets of numbers, where each input has a unique output. It is represented by an equation or a graph.
To find a function given a limit and restriction, you can use the limit definition of a derivative. This involves taking the limit of the difference quotient as the input approaches the given limit. You can then use algebraic manipulation to solve for the function.
A limit is a mathematical concept that describes the behavior of a function as the input approaches a certain value. It is represented by the notation lim f(x), where x represents the input and f(x) represents the function.
Restrictions in a function refer to limitations or conditions that are placed on the input or output of the function. These can include domain and range restrictions, as well as constraints on the type of function (e.g. polynomial, exponential, etc.).
Yes, a function can have multiple limits and restrictions. In fact, many real-world functions have multiple constraints and limitations that must be considered when finding a function. It is important to carefully analyze and understand all the restrictions in order to accurately determine the function.