Explain why functions with the property f (-x) = - f (x) are called odd functions and functions with the property f (-x) = f (x) are called even functions.

The functions with the property f (-x) = f (x) are called even functions because they symmetric about the y-axis and The functions with the property f (-x) = - f (x) are called odd because these function are symmetric about the origin.

Step-by-step explanation:

The functions with the property f (-x) = f (x) are called even functions because they symmetric about the y-axis. In other words these functions usually take a form x^2, x^4, x^6, x^8 etc. However, there are other functions that behave like that too, such as cos (x). An even exponent does not always make an even function, for example (x+1) ^2 is not an even function.

The functions with the property f (-x) = - f (x) are called odd because these function are symmetric about the origin. In other words they are called odd because of the functions like x, x^3, x^5, x^7, etc. but there are other functions that behave like that, too, such sin (x). but an odd exponent does not always make an odd function, for example x3+1 is not an odd function.