The x-intercepts are the points where the graph of the function intersects the x-axis. At these points, the value of y is zero. Therefore, to find the x-intercepts, we set f(x) = 0 and solve for x....
f(x) = (x − 3)(x − 2)(x − 1) = 0
For the product of three factors to be zero, at least one of the factors must be zero. Therefore, we have three possible cases:
x - 3 = 0 or x - 2 = 0 or x - 1 = 0
Solving for x in each case, we get:
x = 3 or x = 2 or x = 1
Therefore, the x-intercepts of the graph of f(x) are (3, 0), (2, 0), and (1, 0).
Y-intercept
The y-intercept is the point where the graph of the function intersects the y-axis. At this point, the value of x is zero. Therefore, to find the y-intercept, we set x = 0 and evaluate f(x).
f(0) = (0 − 3)(0 − 2)(0 − 1) = (-3)(-2)(-1) = -6
Therefore, the y-intercept of the graph of f(x) is (0, -6).
Summary
The x-intercepts of the graph of f(x) = (x − 3)(x − 2)(x − 1) are (3, 0), (2, 0), and (1, 0). The y-intercept of the graph of f(x) is (0, -6).