# 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 $y=f(x)$ right... What does this mean?

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

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

For definiteness:

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

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

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

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

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

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

For instance, saying that $y$ is function of $x$ by the function $y = x^2$, we see that by choosing a value for $x$, we immediately obtain another value for $y$ which is function of $x$ 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 $y$ is function of $x$, then choosing a value for $x$ will yield a (or possibly more) value(s) for $y$ by this particular mapping which actually is the function.

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