Consider the function represented by the equation $x-y=3$. What is the equation written in function notation, with $x$ as the independent variable?

A. $f(x)=y+3$
B. $f(x)=-y-3$
C. $f(x)=-x+3$
D. $f(x)=x-3$

Solve the equation x − y = 3 for y in terms of x .
Subtract x from both sides to get − y = 3 − x .
Multiply both sides by − 1 to get y = x − 3 .
Express the equation in function notation: f ( x ) = x − 3 ​

Explanation

Understanding the Problem We are given the equation x − y = 3 and we want to express it in function notation, f ( x ) , where x is the independent variable. This means we need to solve for y in terms of x .

Isolating y To solve for y , we can start by isolating y on one side of the equation. We have x − y = 3

Subtracting x Subtract x from both sides: − y = 3 − x

Multiplying by -1 Multiply both sides by − 1 :
y = x − 3

Function Notation Now, we can replace y with f ( x ) to express the equation in function notation: f ( x ) = x − 3

Final Answer Therefore, the equation in function notation is f ( x ) = x − 3 .


Examples
In physics, if you know that the distance an object travels is its initial position minus 3 meters, this function can help you quickly determine the distance based on the initial position. For example, if the initial position x is 10 meters, then the distance f ( x ) is 10 − 3 = 7 meters. This kind of function is useful in various scenarios where one variable depends linearly on another.

Answered by GinnyAnswer | 2025-07-03