Final answer:
To sketch the function f(x) = -4x^5 - x + 3, plot several points considering the dominance of the -4x^5 term for large x values, which makes the ends of the graph open downward.
Step-by-step explanation:
The question requires sketching the graph of the given function f(x) = -4x5 - x + 3. To do this, you can plot several points by choosing values for x and calculate the corresponding f(x). However, for sketching purposes and understanding the behavior of the function, it is important to note that the leading term is -4x5 which indicates that as x increases or decreases without bound, f(x) will also increase or decrease sharply due to the fifth power, with a negative coefficient causing a downward opening on both ends.
The function is an odd-degree polynomial, which implies that its ends go off in opposite directions (the right end going down and the left end going up). Due to the -4x5 dominance for large values of x, the -x and +3 terms have negligible effect on the overall shape of the curve but can affect the graph near the origin where x is small.