Final answer:
The x-intercepts of the function f(x) = (x-1)(x-2)(3x³) are 1, 2, and 0. The y-intercept of the function is 0.
Step-by-step explanation:
The x-intercepts of a function occur when the y-value is equal to zero. To find the x-intercepts of the function f(x) = (x-1)(x-2)(3x³), we set the function equal to zero and solve for x:
(x-1)(x-2)(3x³) = 0
This equation has three solutions: x = 1, x = 2, and x = 0 (which comes from the factor 3x³ = 0). Therefore, the x-intercepts are 1, 2, and 0.
The y-intercept of a function occurs when x is equal to zero. To find the y-intercept of the given function, we substitute x = 0 into the function:
f(0) = (0-1)(0-2)(3(0)³) = (-1)(-2)(0) = 0
Therefore, the y-intercept of the function is 0.