Question

consider the function represented by the equation ( x - y = 3 ). what is the equation written in function notation, with ( x ) as the independent variable?
( \bigcirc ) ( f(x) = y + 3 )
( \bigcirc ) ( f(x) = -y - 3 )
( \bigcirc ) ( f(x) = -x + 3 )
( \bigcirc ) ( f(x) = x - 3 )

Explanation:

Step1: Solve the equation for y

We start with the equation \( x - y = 3 \). To solve for \( y \), we can subtract \( x \) from both sides and then multiply by -1.
Subtract \( x \) from both sides: \( -y = 3 - x \)
Multiply both sides by -1: \( y = x - 3 \)

Step2: Replace y with f(x)

In function notation, when \( x \) is the independent variable, we write \( y = f(x) \). So we replace \( y \) with \( f(x) \), giving \( f(x)=x - 3 \).

Answer:

D. \( f(x) = x - 3 \)