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?

Answer 1

To write the equation x - y = 3 in function notation with x as the independent variable, we solve for y to get f(x) = x - 3, where f(x) represents the dependent variable y as a function of x.

Step-by-step explanation:

The student has asked about converting the equation x - y = 3 into function notation with x as the independent variable. To write this equation in function notation, we first solve for y.

Starting with the equation x - y = 3, we want to isolate y on one side:

• Add y to both sides: x = y + 3.
• Subtract 3 from both sides: x - 3 = y.

Therefore, written in function notation where y is the dependent variable and x is the independent variable, the equation becomes f(x) = x - 3.

In function notation, the dependent variable is typically represented as f(x), which denotes that y is a function of x. This is a common way to express equations in algebra and helps to clearly indicate which variable is dependent on the other.

Answer 2

When the question asks to write the equation "in function notation, with
`x` as the independent variable?", it simply is asking for the isolation of
`y`. This means that
`y` must be on its own side of the = sign with everything else on the other, because the dependent variable is being affected by the independent variable (hence the name "dependent").

The first step is to subtract
`x` from both sides, so you end up with
`-y=3-x`. This may look finished, but
`y` is still attached to a negative sign. To fix this, we must divide both sides by
`-1` to receive our final answer of
`y=-3+x`, which, when rearranged to be written in proper notation, reads as:


`y=x-3`

Hope I could help! :)