Answer: (1,0), (2,0), and (4,0); (0, -8)
Step-by-step explanation:
The x-intercept is the point where the graph will cross the x-axis, so y=0. We can solve for x here by setting f(x) to 0.
[tex]0 = (x-4)(x-2)(x-1)\\\( x = 4 \) or \( x = 2 \) or \( x = 1 \)[/tex]
From here, we know that the x-intercepts are (1,0), (2,0), and (4,0).
The y-intercept is the point where the graph will cross the y-axis, so x=0.
We can solve for y here by setting x to 0.
[tex]y = (0 - 4)(0 - 2)(0 - 1)\\= -8[/tex]
From here, we know that the y-intercept is (0, -8).