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The problem asks why the graph of \( y^2 = x^2 \) is not a graph of a function of \( x \).

### Let's analyze this equation:
1. **Given equation:** \( y^2 = x^2 \).
2. **Rewrite equation:** We can rewrite this as \( y^2 = x^2 \) implies \( y = \pm x \). 

This implies that for each value of \( x \), there are two possible values for \( y \): \( y = x \) or \( y = -x \).

### Answering the question:
- A function, by definition, assigns exactly one value of \( y \) for each value of \( x \). 
- However, in this case, for each nonzero value of \( x \), there are two corresponding values of \( y \). This violates the definition of a function.

### Conclusion:
The correct answer is **D**: "For each nonzero value of \( x \), there are two values of \( y \)."

Would you like more details or have any questions about this explanation?

Here are five related questions you might find interesting:
1. What is the definition of a function?
2. How do you determine if a relation is a function using the vertical line test?
3. Can a function have two values of \( x \) for a single value of \( y \)?
4. What are some examples of relations that are not functions?
5. How would the graph of \( y^2 = x^2 \) look on the coordinate plane?

**Tip:** When analyzing whether a relation is a function, always check if a single input (x-value) produces more than one output (y-value).

Why is the graph of y^2 = x^2 not a graph of a function of x?

Explore why the graph of the equation y^2 = x^2 is not considered a function of x. This explanation covers key algebraic concepts, the definition of functions, and how to analyze equations to determine whether they meet the criteria of a function.

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