Final answer:
The x-intercepts of the equation f(x) = (x - 4)(x + 1)(x + 8) are 4, -1, and -8, and the y-intercept is at the point (0, -32) on the graph.
Step-by-step explanation:
To find the x-intercepts of the function f(x) = (x - 4)(x + 1)(x + 8), we need to determine the values of x that make the function equal to zero. These are the points where the graph of the function crosses the x-axis. Setting the function f(x) equal to 0, we get:
0 = (x - 4)(x + 1)(x + 8)
The function equals zero when x is 4, -1, or -8. Therefore, the x-intercepts are at x = 4, x = -1, and x = -8.
To find the y-intercept, we set x to zero in the function and solve for f(0):
f(0) = (0 - 4)(0 + 1)(0 + 8) = -4 × 1 × 8 = -32
So, the y-intercept is at (0, -32).
In conclusion, the x-intercepts of the function are 4, -1, and -8, and the y-intercept is -32.