# How can you determine the end behavior of a function?

| May 27, 2018

You can determine the end behavior of a function by looking at the degree of the function and the sign of the leading coefficient.
What is the degree of the function? The degree of a function is the highest exponent.
What is the sign of the leading coefficient? The leading coefficient is the number coefficient (number in front of) the term with the highest degree. The sign is either positive or negative.
There are four possible options for end behavior.
Option 1: The degree is even and the leading coefficient is positive. In this case, the end behavior is up at the far left and up at the far right.
Option 2: The degree is even and the leading coefficient is negative. In this case, the end behavior is down at the far left and down at the far right.
Option 3: The degree is odd and the leading coefficient is positive. In this case, the end behavior is down at the far left and up at the far right.
Option 4: The degree is odd and the leading coefficient is negative. In this case, the end behavior is up at the far left and down at the far right.

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