Answer:
"even."
Explanation:
An even function is a symmetrical function that has an axis of symmetry along the y-axis, meaning that the function's value at a particular x-coordinate is equal to its value at the opposite x-coordinate. In mathematical terms, this can be represented as f(x) = f(-x).
For example, the function f(x) = x^2 is an even function. If we take any x-value, such as x = 2, the function evaluates to f(2) = (2)^2 = 4. If we take the opposite x-value, which is x = -2, the function also evaluates to f(-2) = (-2)^2 = 4. Therefore, the function has symmetry along the y-axis.
In contrast, an odd function is a symmetrical function that has an axis of symmetry at the origin, meaning that the function's value at a particular x-coordinate is equal in magnitude but opposite in sign to its value at the opposite x-coordinate. An odd function can be represented as f(x) = -f(-x).
To summarize, in the given question, the symmetrical function that has an axis of symmetry along the y-axis, such that f(x) = f(-x), is an even function.