What is the end behavior of the graph of the polynomial function f of x is equal to 3 x to the 6th power plus 30 x to the 5th power plus 75 x to the 4th power ?

The end behavior is determined by the leading term, 3x^6. Its degree is even, so both ends of the graph go in the same direction. Its leading coefficient is positive, so both ends rise: as x approaches negative infinity, y approaches positive infinity, and as x approaches positive infinity, y also approaches positive infinity. This matches choice C.

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