Find any points of discontinuity for each rational
function. Sketch the graph. Describe any vertical or
horizontal asymptotes and any holes.
19.y=x-1/(x+2)(x-1)
20.y=x*3-1/x*2-1
21.y=2x*2+3/x*2+2
19. The rational function y = (x-1)/(x+2)(x-1) has points of discontinuity at x = -2 and x = 1, where the denominators of the rational expression equal zero. At x = -2 and x = 1, the rational function has vertical asymptotes.
The function has a hole at x = 1, as the factor (x-1) cancels out in both the numerator and denominator.
20. The rational function y = (3x-1)/(2x-1) has a point of discontinuity at x = 1/2, where the denominator of the rational expression equals zero. At x = 1/2, the rational function has a vertical asymptote.
21. The rational function y = (2x^2+3)/(x^2+2) does not have any points of discontinuity, as the denominator does not equal zero for any real value of x. The function has no vertical asymptotes.
Please note that without specific values or a graph, it is difficult to provide an accurate sketch of the graph or accurate description of asymptotes and holes.