Final answer:
The domain of the function is all real numbers, the range is all real numbers, there are no x-intercepts, and the y-intercept is (0, 9).
Step-by-step explanation:
The given function is y = x4 + 4x3 - 2x2 - 12x + 9.
a. The domain of a function represents all possible input values (x-values) for which the function is defined. In this case, there are no restrictions on the input values, so the domain is all real numbers (-∞, ∞).
b. The range of a function represents all possible output values (y-values) that the function can take. As the function is a polynomial, it will have a range of all real numbers (-∞, ∞).
c. The x-intercepts are the points where the graph of the function intersects the x-axis. To find these points, set y = 0 and solve for x. In this case, there is no real solution, so there are no x-intercepts.
d. The y-intercept is the point where the graph of the function intersects the y-axis. To find this point, set x = 0 and solve for y. In this case, when x = 0, y = 9, so the y-intercept is (0, 9).