is y=4x^2 a function yes or no explain why?

**Yes**, \( y = 4x^2 \) is a function.

### Explanation:
- **Definition of a Function**: A function is a relation where every input (value of \( x \)) has exactly one output (value of \( y \)).
- In the equation \( y = 4x^2 \), for every value of \( x \) that you substitute into the equation, you will get exactly one corresponding value of \( y \).
- There are no inputs (values of \( x \)) that produce more than one output (value of \( y \)). This means that for each \( x \), there is a unique \( y \), which satisfies the condition of being a function.

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**Related Questions:**

1. What is the definition of a function in mathematics?
2. How can you determine if a relation is a function by looking at a graph?
3. What is the domain of the function \( y = 4x^2 \)?
4. What is the range of the function \( y = 4x^2 \)?
5. How does the equation \( y = 4x^2 \) describe the shape of its graph?
6. Can you provide an example of a relation that is not a function?
7. How does the graph of \( y = 4x^2 \) compare to \( y = x^2 \)?
8. What is the vertex of the parabola represented by \( y = 4x^2 \)?

**Tip:** Use the vertical line test to quickly check if a graph represents a function. If any vertical line crosses the graph more than once, the relation is not a function.

Understand why y = 4x^2 is a function through clear explanations and examples. Learn about the definition of a function in mathematics and how it applies to quadratic equations. Suitable for high school students studying functions and algebra.

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