So, how to find end behavior of a function? We decide end behavior on the basis of degree of function and also the most prominent coefficient in the polynomial function.
Most prominent or noticeable coefficient in the polynomial is defined as that noteworthy figure when compared to additional coefficients in the function for having either a very huge or very insignificant value. The sign of coefficient is enough to guess the end behavior of the function. Let us consider an example to understand this concept:
Q. Judge the end behavior of the polynomial function given as follows: u4 – 4 u3 + 3 u + 25?
Solution: In the given polynomial function we can find the degree to be 4, which is an even figure and so leading coefficient will be of the term with power 4 only i.e. 1. We see that leading coefficient is also + ve. So, end behavior of polynomial function can be defined as:
F (u) → + ve infinity, as u → - ve infinity and
F (u) → + ve infinity, as u → + ve infinity
Graph of u4 – 4u3 + 3 u + 25 also shows the end behavior of function as: