# What is the graph of $f(y)=cy$?

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Erdos
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• Let me know if you need any clarifications.

• Erdos, I appreciate the response. So in your example, did you set y=f(y). Or you just labeled the horizontal axis as f(y). In the set definition, wouldn't it be (y, f(y): y is in R) for the pairs?

• I added some more details.

• Great! One last thing . Suppose that the input is now x+y=u. Is this also valid: Graph of f = {(u,v) ∈ R×R : v = f(u)} is equal to {(x,y)∈R×R:y=f(x)}.

• Your question does not make much sense. In the equation x+y=u there are three variables. You should have two variables in the equation of the graph of a function.

• I am sorry about that. I hope I can clarify. What if we add two real values, x and y. Is it true that the addition of two real numbers = another real number. Then apply the function to that new variable which is composed of the addition of two real variables? Can we graph this new variable?

• For example: f(x+y)=c(x+y).

• Erdos
+1

In this case you can set z=x+y, and the equation can still be written as f(z)=cz. The graph will be the same. If you define f(x,y)=c(x+y) then this is a function of two variables x and y whose graph is a surface in three dimensions, but I think this is outside of the scope of your question.

• Yes it would be. So then we would set up the graph to be the vertical axis as v and the horizontal axis as u. Therefore this statement would be true: Graph of f = {(u,v) ∈ R×R : v = f(u)}. I should have set that expression equal to another variable as there are only two variables in the equation of the graph of a function. I understand now.

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