What is left and right hand behavior?

The left-hand behavior, as x approaches negative infinity, is for the function to decrease without bound as a negative raised to an odd power is negative. The right-hand behavior, as x approaches positive infinity, is for the function to increase without bound as a positive raised to a positive value is positive.

The left hand behavior of a polynomial function. If the degree of the polynomial is Odd, the left hand Changes from the right hand. If the degree of the polynomial is Even, the left hand does the Same as the right hand.