Question

How to know if a function is even or odd.

Answer 1

An even function is a function that satisfies the condition y(x) = y(-x), while an odd function is a function that satisfies the condition y(x) = -y(-x). By determining whether a function satisfies these conditions, you can determine if it is even or odd.

Step-by-step explanation:

An even function is a function that satisfies the condition y(x) = y(-x). This means that if you replace x with -x in the function and the resulting function is unchanged, then the function is even. On the other hand, an odd function is a function that satisfies the condition y(x) = -y(-x). This means that if you replace x with -x in the function and the resulting function is the negative of the original function, then the function is odd.

For example, the function f(x) = x^2 is even because f(-x) = (-x)^2 = x^2 = f(x). The function g(x) = x^3 is odd because g(-x) = (-x)^3 = -x^3 = -g(x).

By determining whether a function satisfies these conditions, you can determine if it is even or odd.

Answer 2

An even function is a function that satisfies the condition y(x) = y(-x), while an odd function is a function that satisfies the condition y(x) = -y(-x). By determining whether a function satisfies these conditions, you can determine if it is even or odd.

Step-by-step explanation:

An even function is a function that satisfies the condition y(x) = y(-x). This means that if you replace x with -x in the function and the resulting function is unchanged, then the function is even. On the other hand, an odd function is a function that satisfies the condition y(x) = -y(-x). This means that if you replace x with -x in the function and the resulting function is the negative of the original function, then the function is odd.

For example, the function f(x) = x^2 is even because f(-x) = (-x)^2 = x^2 = f(x). The function g(x) = x^3 is odd because g(-x) = (-x)^3 = -x^3 = -g(x).

By determining whether a function satisfies these conditions, you can determine if it is even or odd.