To rewrite the given equation [tex]\( x - y = 3 \)[/tex] in function notation with [tex]\( x \)[/tex] as the independent variable, follow these steps:
1. Isolate [tex]\( y \)[/tex] in the equation:
[tex]\[
x - y = 3
\][/tex]
Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[
-y = 3 - x
\][/tex]
Multiply through by -1 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = -(3 - x) = x - 3
\][/tex]
2. Express [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex]:
By isolating [tex]\( y \)[/tex], we have determined that [tex]\( y = x - 3 \)[/tex]. In function notation, we typically write the dependent variable (in this case, [tex]\( y \)[/tex]) as [tex]\( f(x) \)[/tex].
Thus, the equation in function notation, with [tex]\( x \)[/tex] as the independent variable, is:
[tex]\[
f(x) = x - 3
\][/tex]
Therefore, the correct equation is [tex]\( f(x) = x - 3 \)[/tex].
Hence, the right answer is:
[tex]\[
\boxed{f(x) = x - 3}
\][/tex]
