Question

F(x) = 2x3 is an odd function. f(x) = − 4 is an even function.

Answer 1

An odd function satisfies the property y(x) = -y(-x), while an even function satisfies the property y(x) = y(-x). By substituting values of x with their negative counterparts, we can determine whether a function is odd or even.

Step-by-step explanation:

An odd function is a function that satisfies the property y(x) = -y(-x). This means that if we substitute any value of x with its negative counterpart in the function, the resulting function should have the opposite sign.

For example, if we have the function f(x) = 2x^3, we can check if it is odd by substituting -x for x: f(-x) = 2(-x)^3 = -2x^3 = -f(x).

Since the function negates itself when x is replaced with -x, we can conclude that f(x) = 2x^3 is odd.

On the other hand, an even function is a function that satisfies the property y(x) = y(-x). This means that if we substitute any value of x with its negative counterpart in the function, the resulting function should remain the same.

For example, if we have the function g(x) = -4, we can check if it is even by substituting -x for x: g(-x) = -4 = g(x).

Since the function remains unchanged when x is replaced with -x, we can conclude that g(x) = -4 is even.