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

• Miike012
In summary, the phrase "y as a function of x" means that the value of y is dependent on the value of x, with x being the independent variable. To be a function, each value of y must have only one corresponding value for x. In the given problem, "f(x)=2x" represents y as a function of x and "u = 2x" is a re-written version. There is also a statement about y' and cu' that needs to be proven, as discussed in the linked conversation.
Miike012

## Homework Statement

What exactly does it mean when the phrase " y as a function of x" mean?

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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