Final answer:
The end behavior of the function f(x) = -3x⁴ + 4x² - 19x + 6 is that the graph decreases and approaches negative infinity as x approaches positive and negative infinity.
Step-by-step explanation:
The end behavior of a function describes the behavior of the graph of the function as x approaches positive infinity and negative infinity. In this case, the function is f(x) = -3x⁴ + 4x² - 19x + 6.
As x approaches positive infinity, the leading term, -3x⁴, dominates the function. Since the power of x is even and the leading coefficient is negative, the graph of the function will be decreasing and approach negative infinity.
As x approaches negative infinity, the leading term, -3x⁴, dominates the function. Again, since the power of x is even and the leading coefficient is negative, the graph of the function will be decreasing and approach negative infinity.