Plot the x - and y - intercepts of the function.

f (x) = x3+2x2-x-2

see below for a plot

Step-by-step explanation:

The y-intercept is where x=0:

f (0) = 0^3 + 2·0^2 - 0 - 2 = - 2

The x-intercepts can be found where f (x) = 0:

0 = x^3 + 2x^2 - x - 2 = x^2 (x + 2) - 1 (x + 2) = (x^2 - 1) (x + 2)

0 = (x + 1) (x - 1) (x + 2)

The values of x that make these factors zero are {-2, - 1, 1}.

The x-intercepts are (-2, 0), (-1, 0), (1, 0). The y-intercept is (0, - 2).