Sketch the graph of y = (x - 3)*(x + 1) (x - 1) by finding its intercepts and its limits as X - co and x - -0, SOLUTION The y-intercept is f(0) = (-3)4(x ) (-1) = [x and the x-intercepts are found by setting y = 0: x = 3, 1, . Notice that since (x - 3)4 is positive, the function doesn't change sign at 3; thus the graph doesn't cross the x-axis at 3. The graph crosses the axis at -1 and When x is large positive, all three factors are positive, so x -+ 0o lim (x - 3) (x + 1)5 (x - 1) = 0. When x is large negative, the first factor is large positive and the second and third factors are both large negative so lim (x - 3)(x + 1)5 ( x - 1) = 0. x - -00 Combining this information, we give a rough sketch of the graph in the figure below. X 3 -81