Functions-Domains,Ranges and Subsets.

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The discussion focuses on understanding functions, specifically regarding domains, ranges, and subsets. The first problem involves determining the largest subset of real numbers for the domain of the function defined by the equation y = 5 - x and whether the function is onto if set A equals set B. The second problem asks how to identify if a graph represents a function and how to determine its domains and ranges without visual aid. Participants express confusion about the concepts of subsets and functions, suggesting a need for clearer explanations. Overall, the thread highlights the challenges in grasping these fundamental mathematical concepts.
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Homework Statement


Can you please explain in as much detail as possible the two following problems?
1.Each set is a function from set A to set B. a.What is the largest subset of the real numbers that can be set A, the domain of the given function? b. If set A=set B, is the function onto? Justify your answer. The problem is {x,y):y=5-x}.

2.For the next problem I can't actually show you the graph but I have to determine if the graph represents a function and I have to state the domains and ranges. How would I do this on a graph?

And what exactly is a subset?

Homework Equations



None.

The Attempt at a Solution


I couldn't even seem to wrap my head around the problem. I just couldn't figure it out. I stared at it for about an hour and I still couldn't understand it.
 
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Do a Wikipedia on what a subset and a function is.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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