Question

Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be written using function notation?

Answer 1

f(x)=______x+4

Answer 2

Well, since it's a lineal equation, we can represent it as a line, and always, ALWAYS we define the function of "x" as the "y" value we acquire for assigning a value to it.

I'll be a little clearer. we always call "x" as the independant variable because we can assign any value we want to it, an we call "y", the dependant variable because depending on the value we assign to "x", is the value we get for "y".
Mathematicians then defined a "function" of x as all the "y" values we can obtain and represent in a reference system.
Thus, they defined f(x)=y.
So what we will do to represent a mathematical expression on "function notation" we solve the expression for "y" and then we change "y" for "f(x)".
so, in your mathematical expression:
\[9x+3y=12\]
We will solve it for "y":
\[y=\frac{ -9x+12 }{ 3 }\]
\[y=\frac{ -9 }{ 3 }x+\frac{ 12 }{ 3 }\]
\[y=-3x+4\]
But, since y=f(x) then:
\[f(x)=-3x+4\]