Describe the right-hand and the left-hand behavior of the graph of t(x)= 4x^5 - 7x^3 - 13

The end behavior of a function behaves as if only the highest order variable existed.

In this case only the behavior of 4x^5 determines the end behavior of the function.

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.

Think of it as five or above give it a shove. change the 5 or above to the right to a zero and add one to the number on the left.