Answer :
To rewrite the given equation \( x - y = 3 \) in function notation with \( x \) as the independent variable, follow these steps:
1. Start with the given equation:
[tex]\[ x - y = 3 \][/tex]
2. Solve for \( y \):
[tex]\[ -y = 3 - x \][/tex]
3. Multiply both sides by \( -1 \) to isolate \( y \):
[tex]\[ y = x - 3 \][/tex]
4. To express this as a function \( f(x) \), we write:
[tex]\[ f(x) = x - 3 \][/tex]
Among the given multiple-choice options:
a) \( f(x) = y + 3 \)
b) \( f(x) = -y - 3 \)
c) \( f(x) = -x + 3 \)
d) \( f(x) = x - 3 \)
The correct answer is:
[tex]\[ \boxed{f(x) = x - 3} \][/tex]
1. Start with the given equation:
[tex]\[ x - y = 3 \][/tex]
2. Solve for \( y \):
[tex]\[ -y = 3 - x \][/tex]
3. Multiply both sides by \( -1 \) to isolate \( y \):
[tex]\[ y = x - 3 \][/tex]
4. To express this as a function \( f(x) \), we write:
[tex]\[ f(x) = x - 3 \][/tex]
Among the given multiple-choice options:
a) \( f(x) = y + 3 \)
b) \( f(x) = -y - 3 \)
c) \( f(x) = -x + 3 \)
d) \( f(x) = x - 3 \)
The correct answer is:
[tex]\[ \boxed{f(x) = x - 3} \][/tex]
