Final answer:
To sketch a possible graph for the polynomial function described, we need to consider the degree and the zeros of the function. The given polynomial function has a degree of 4 and the zeros are -3, 4, and 6. We can sketch the possible graph by plotting these zeros on the x-axis and considering the end behavior of the function.
Step-by-step explanation:
The given polynomial function has a degree of 4 and the zeros are -3, 4, and 6. If a quadratic function has a zero at x = a, then x - a is a factor of the function. So, for this polynomial, the factors would be (x + 3), (x - 4), and (x - 6). We can sketch the possible graph by plotting these zeros on the x-axis and considering the end behavior of the function.
Since the degree of the polynomial is 4, the graph will either approach positive infinity or negative infinity in the far ends of the x-axis. However, the statement mentioned that as x gets larger and larger in either the positive or the negative direction, y gets larger and larger in the negative direction. This means that the end behavior of the graph is as follows:
- As x approaches negative infinity, y approaches negative infinity.
- As x approaches positive infinity, y approaches negative infinity.