What Is The End Behavior Of The Graph Of The Polynomial Function F(X) = 3X⁶ + 30X⁵ + 75X⁴?

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) = 3x⁶ + 30x⁵ + 75x⁴ 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, 3x⁶. As x tends towards negative infinity, the value of 3x⁶ tends towards positive infinity, and as x tends towards positive infinity, the value of 3x⁶ tends towards negative infinity. This behavior is also reflected in the value of 3x⁶ + 30x⁵ + 75x⁴, 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) = 3x⁶ + 30x⁵ + 75x⁴ is to approach positive infinity as x tends towards negative infinity, and to approach negative infinity as x tends towards positive infinity.