# Thread: what is : "one variable being a function of another.

1. ## what is : "one variable being a function of another.

I'm preparing to take an exemption test which will allow me to bypass intermediate/pre-algebra and go into college algebra (math 1111_
..one of the stated objectives i should know is:
"Define the concept of one variable being a function of another."
- i have the textbook for the course I'm trying to bypass and am grinding away, but thought someone may expand on this concept.
thank you

2. So we have $\displaystyle y=f(x)$ right... What does this mean?

$\displaystyle x$ is a number. Think of $\displaystyle x$ in terms of the $\displaystyle x-axis;$ it take on values $\displaystyle (-\infty, \infty).$

Then $\displaystyle f(x)$ is a mapping of $\displaystyle x.$ It takes the values of $\displaystyle x$ and transforms them to take on new properties.

For definiteness:

we have $\displaystyle f(x)=x^2.$

Again $\displaystyle x$ is just the Real line: $\displaystyle (-\infty, \infty).$

$\displaystyle f(x)$ on the other hand, takes on the properties of a parabola. Also, it can only yield positive values, so its range is restricted to $\displaystyle [0,\infty).$

So as we feed $\displaystyle f(x)$ input values, $\displaystyle x,$ it transforms them to take on these new properties as described above.

When we set $\displaystyle y$ equal to $\displaystyle f(x)$ we are assigning a variable to the transformed values. So $\displaystyle y$ is a variable that is a function of $\displaystyle x.$

3. It basically means that one variable is linked to another in a one-way (or possibly bijective) mapping. That is, if variable $\displaystyle y$ is function of $\displaystyle x$, then choosing a value for $\displaystyle x$ will yield a (or possibly more) value(s) for $\displaystyle y$ by this particular mapping which actually is the function.

For instance, saying that $\displaystyle y$ is function of $\displaystyle x$ by the function $\displaystyle y = x^2$, we see that by choosing a value for $\displaystyle x$, we immediately obtain another value for $\displaystyle y$ which is function of $\displaystyle x$ via this function.

Does it make sense ?
I think I confused you more than helped you didn't I

4. Originally Posted by Bacterius
It basically means that one variable is linked to another in a one-way (or possibly bijective) mapping. That is, if variable $\displaystyle y$ is function of $\displaystyle x$, then choosing a value for $\displaystyle x$ will yield a (or possibly more) value(s) for $\displaystyle y$ by this particular mapping which actually is the function.

For instance, saying that $\displaystyle y$ is function of $\displaystyle x$ by the function $\displaystyle y = x^2$, we see that by choosing a value for $\displaystyle x$, we immediately obtain another value for $\displaystyle y$ which is function of $\displaystyle x$ via this function.

Does it make sense ?
I think I confused you more than helped you didn't I
I love how we both independently choose f(x)=x^2.

5. yes, that is the understanding which i initially held....for whatever reason the phrasing
"Define the concept of one variable being a function of another."

caused me uncertainty and raised the question: "what did I miss?"...
thank you both, very clear

6. Originally Posted by Anonymous1
I love how we both independently choose f(x)=x^2.
Me too