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

### Explanation:
A function is a relation where each input (or value of \( x \)) is associated with exactly one output (or value of \( y \)). In mathematical terms, for every \( x \) in the domain, there is only one corresponding \( y \).

For the equation \( y = 4x^2 \):
- **Input (x)**: You can choose any real number as the input.
- **Output (y)**: For each \( x \) value, \( y \) is calculated as \( 4x^2 \).

Because the square of a number is always non-negative and the multiplication by 4 is a simple arithmetic operation, each input \( x \) will produce exactly one output \( y \). There are no cases where a single \( x \) produces multiple \( y \) values, which satisfies the condition of being a function.

### Key Points:
- **Single Output**: For every \( x \), there's only one \( y \).
- **Parabola Shape**: The graph of this function is a parabola that opens upwards, indicating that for each \( x \), there’s a single corresponding \( y \) value.

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**Related Questions:**

1. What is the domain of the function \( y = 4x^2 \)?
2. What is the range of the function \( y = 4x^2 \)?
3. How does the graph of \( y = 4x^2 \) compare to the graph of \( y = x^2 \)?
4. What are the vertex and axis of symmetry of the parabola \( y = 4x^2 \)?
5. How would you determine if a relation is not a function?
6. What happens to the graph of \( y = 4x^2 \) if the equation changes to \( y = -4x^2 \)?
7. How can you test if an equation represents a function using the vertical line test?
8. How would the function \( y = 4x^2 + 3 \) be graphed?

**Tip:** When checking if a relation is a function, consider if each input has a unique output. If any input corresponds to multiple outputs, it is not a function.

Explore whether the equation y = 4x^2 is a function with a detailed explanation. Understand the criteria for a function and how this quadratic equation fits. Suitable for students in Grades 9-12.

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