Final answer:
The equation y² = 2x² - 1 is not a function because it assigns multiple y-values to a single x-value, failing the Vertical Line Test, and its form does not correspond to an even or odd function.
Step-by-step explanation:
To determine if the equation y² = 2x² - 1 represents a function, we need to consider the definition of a function. A function is a relation in which each input (usually x) assigns exactly one output (usually y). When we solve for y in the given equation, we get two solutions for y, one positive and one negative for each nonzero value of x, suggesting that multiple outputs (y-values) correspond to a single input (x-value). This means the equation does not represent a function in the conventional sense because it fails the Vertical Line Test; if you draw a vertical line through any point on the graph, it will intersect the graph at more than one point.
Additionally, we can look at the equation from the perspective of even and odd functions. An even function is symmetric about the y-axis and satisfies the condition y(x) = y(-x), while an odd function is symmetric about the origin and satisfies the condition y(x) = -y(-x). The original equation does not satisfy these conditions for either even or odd functions.