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?

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.