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

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Homework Help Overview

The discussion revolves around the interpretation of the phrase "y as a function of x" and its implications in mathematical expressions. Participants explore the relationship between independent and dependent variables in the context of functions.

Discussion Character

  • Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the definition of a function, the relationship between x and y, and how to rewrite expressions involving functions. Questions arise about whether different parts of a problem are connected and how to interpret them correctly.

Discussion Status

The conversation is ongoing, with participants seeking clarification on the relationship between various expressions and the requirements for functions. Some guidance has been offered regarding the nature of functions, but there is no explicit consensus on the connections between the problem components.

Contextual Notes

Participants note the importance of stating problems verbatim and question the completeness of the information provided in the original problem statement.

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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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