https://file.aiquickdraw.com/mathbot/file/1724691607439vcyadcy2.jpg

The equation in the image is:

\[
S^2 + T = 3x - T - y
\]

To rewrite this relation as a function of \( x \), let's solve for \( x \) in terms of the other variables \( S \), \( T \), and \( y \).

1. First, isolate the term involving \( x \):
\[
S^2 + T + T = 3x - y
\]
\[
S^2 + 2T = 3x - y
\]

2. Next, solve for \( 3x \) by adding \( y \) to both sides:
\[
3x = S^2 + 2T + y
\]

3. Finally, solve for \( x \) by dividing everything by 3:
\[
x = \frac{S^2 + 2T + y}{3}
\]

So the relation expressed as a function of \( x \) is:

\[
x = \frac{S^2 + 2T + y}{3}
\]

This equation shows \( x \) as a function of \( S \), \( T \), and \( y \).

Would you like any further details or have any questions?

Here are 5 related questions:
1. How would the equation change if \( S \) or \( T \) were isolated?
2. Can this equation be simplified further if any variables are constants?
3. What would the function look like if \( y \) was a function of \( S \) and \( T \)?
4. How does the function behave as \( S \) and \( T \) increase or decrease?
5. What are the implications of this function in a real-world context?

**Tip:** When manipulating algebraic equations, always perform the same operation on both sides of the equation to maintain equality.

Learn how to rewrite a given relation as a function of x with a detailed step-by-step solution. This problem involves algebraic manipulation and function notation, providing insights into solving equations and expressing relations. Suitable for high school students and those interested in algebraic functions.

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