# What Is The End Behavior Of The Graph Of The Polynomial Function F(X) = 3X^{6} + 30X^{5} + 75X^{4}?

The end behavior of a graph of a polynomial function is the direction in which the graph tends to head as *x* approaches positive infinity or negative infinity. The end behavior of the graph of the polynomial function *f(x)* = 3*x*^{6} + 30*x*^{5} + 75*x*^{4} is to approach positive infinity as *x* tends towards negative infinity, and to approach negative infinity as *x* tends towards positive infinity.

To see why this is the case, we can look at the function’s leading term. The leading term is the term with the highest degree – in this case, 3*x*^{6}. As *x* tends towards negative infinity, the value of 3*x*^{6} tends towards positive infinity, and as *x* tends towards positive infinity, the value of 3*x*^{6} tends towards negative infinity. This behavior is also reflected in the value of 3*x*^{6} + 30*x*^{5} + 75*x*^{4}, and so we can conclude that the end behavior of the graph of this function is to approach positive infinity as *x* tends towards negative infinity, and to approach negative infinity as *x* tends towards positive infinity.

In conclusion, the end behavior of the graph of the polynomial function *f(x)* = 3*x*^{6} + 30*x*^{5} + 75*x*^{4} is to approach positive infinity as *x* tends towards negative infinity, and to approach negative infinity as *x* tends towards positive infinity.