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Write F if function and NF if not function in a given problem.

The given equation is \( y + x^2 = 6 \).

To determine if this represents a function, we need to check if for every input \( x \), there is exactly one corresponding output \( y \). 

### Step 1: Solve for \( y \)
Rearranging the equation to solve for \( y \):

\[
y = 6 - x^2
\]

### Step 2: Analyze the relationship

The equation \( y = 6 - x^2 \) indicates that for every value of \( x \), there is exactly one value of \( y \). Therefore, this is a **function** because it passes the vertical line test (each value of \( x \) corresponds to one value of \( y \)).

Thus, the answer is **F** (Function).

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Would you like a deeper explanation or have any questions? Here are five related questions to extend this topic:

1. What is the domain of the function \( y = 6 - x^2 \)?
2. How do you graph the function \( y = 6 - x^2 \)?
3. What is the range of the function \( y = 6 - x^2 \)?
4. What is the vertex of the parabola represented by the equation \( y = 6 - x^2 \)?
5. How would the function change if the equation were \( y + x^3 = 6 \)?

**Tip**: When determining if an equation is a function, always check if each input produces only one output.

Learn how to determine if the equation y + x^2 = 6 represents a function by analyzing its solution and applying the vertical line test. This problem covers key algebraic concepts related to functions and quadratic equations.

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