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To determine if the function \( f(x) = 3 - 2x^2 \) is one-to-one, we can use the horizontal line test. A function is one-to-one if any horizontal line drawn across the graph intersects the function's curve at most once. 

### Analysis
The graph of \( f(x) = 3 - 2x^2 \) is a downward-opening parabola, centered at \( x = 0 \). Since this is a parabolic function with a "U" shape, any horizontal line drawn within the range of \( f(x) \) will intersect the graph in two places (except at the very top, at \( y = 3 \), which intersects only once). Therefore, this function does **not** pass the horizontal line test and is **not one-to-one**.

### Answer
- **No**, the function is not one-to-one.

Would you like further explanation or details on the horizontal line test?

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Here are 5 additional questions related to this concept:
1. How can we tell if a function is one-to-one just by looking at its equation?
2. What is the significance of a function being one-to-one?
3. Can a function be made one-to-one by restricting its domain?
4. How does the vertical line test differ from the horizontal line test?
5. How would the graph of \( f(x) = 3 - 2x^2 \) change if the coefficient of \( x^2 \) were positive?

**Tip:** The horizontal line test only applies to functions and helps to identify if a function has an inverse that is also a function.

Use the horizontal line test to determine whether the function f(x) = 3 - 2x^2 is one-to-one.

Analyze the function f(x) = 3 - 2x^2 to determine if it is one-to-one using the horizontal line test. Learn about parabolas, quadratic functions, and the horizontal line test in this detailed breakdown, suitable for high school math students.

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