Answer:
An odd function is a function that is symmetrical about the origin, meaning that for every x value, there is a corresponding -x value that produces the opposite y value. For example, the function f(x) = x^3 is odd because f(-x) = (-x)^3 = -x^3 = -f(x).
An example of an odd function is f(x) = x^3. An example of an even function is f(x) = x^2. An example of a function that is neither even nor odd is f(x) = x^4.
Explanation:
A quintic function is a polynomial function of degree 5, meaning that it has the form f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f, where a, b, c, d, e, and f are constants. The minimum number of real roots that a quintic function can have is 0, and the maximum is 5. This is because the Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n roots, which can be real or complex.
An even function is a function that is symmetrical about the y-axis, meaning that for every x value, there is a corresponding -x value that produces the same y value. For example, the function f(x) = x^2 is even because f(-x) = (-x)^2 = x^2 = f(x).