Understanding the Meaning of 'y as a Function of x' | Quick & Easy Question

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The phrase "y as a function of x" indicates that the value of y is determined by the value of x, where x serves as the independent variable. In a function, each y value corresponds to exactly one x value, ensuring no two y values share the same x. The expression f(x) = 2x indeed represents y as a function of x. The discussion also raises questions about rewriting the function u in terms of x and the relationship between u and y, specifically in the context of proving that y' = cu'. Understanding these concepts is crucial for solving related mathematical problems effectively.
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Homework Statement


What exactly does it mean when the phrase " y as a function of x" mean?
 
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The value of y depends on the value of x. x is an independent variable and you may choose values for x to use in an expression. The result of using each of the acceptable values of x will produce a resulting value for y.

For an expression to be a function, each value of y can have ONE value for x. No two y values have the same x value.
 
I have this problem in my book that says...
f(x)=2x ( does f(x) mean y as a function of x?)
Then it says
Suppose u is a function of x
How would I re-write the problem?
 
Would I just write it as...
u = 2x?
 
Maybe, but once again you're being guilty of NOT stating the entire problem VERBATIM.
Miike012 said:
I have this problem in my book that says...
f(x)=2x
Then it says
Suppose u is a function of x
Is "f(x)=2x" and "Suppose u is a function of x" part of the same problem? And what does the rest of the problem say?
 
It says...
Suppose that u is a function of x and
y = cu
then what we believe is that y' = cu'

Then it asks me to prove that
y' = cu' is correct.
 
Does anyone know?
 

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