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?

f(x) = y + 3
f(x) = –y – 3
f(x) = –x + 3
f(x) = x – 3

Answer 1

To write the equation \( x - y = 3 \) in function notation with \( x \) as the independent variable, we need to solve for \( y \).

Starting with the given equation:

\[
x - y = 3
\]

We can rearrange it to solve for \( y \):

\[
-y = 3 - x
\]

Now, multiply both sides by -1:

\[
y = x - 3
\]

Now we can express this in function notation, where \( f(x) = y \):

\[
f(x) = x - 3
\]

Thus, the correct answer is:

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