To convert the given equation [tex]\( x - y = 3 \)[/tex] into function notation with [tex]\( x \)[/tex] as the independent variable, we need to solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex].
Here are the steps:
1. Start with the given equation:
[tex]\[
x - y = 3
\][/tex]
2. Isolate [tex]\( y \)[/tex] on one side of the equation:
[tex]\[
x - y = 3
\][/tex]
Subtract [tex]\( x \)[/tex] from both sides to move [tex]\( x \)[/tex] to the right-hand side:
[tex]\[
- y = -x + 3
\][/tex]
3. Multiply both sides by [tex]\(-1\)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[
y = x - 3
\][/tex]
4. Write the equation in function notation:
[tex]\[
f(x) = x - 3
\][/tex]
Therefore, the function in notation form is:
[tex]\[
f(x) = x - 3
\][/tex]
This matches the fourth option given:
[tex]\[
f(x) = x - 3
\][/tex]
Hence, the correct answer is:
[tex]\[
\boxed{4}
\][/tex]
