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
19.
Points of discontinuity: x = -2, x = 1
Vertical asymptotes: x = -2, x = 1
Hole: At x = 1
Sketch:
- There are two vertical asymptotes at x = -2 and x = 1.
- At x = 1, there is a hole in the graph.
- The function approaches zero as x approaches positive or negative infinity.
20.
Points of discontinuity: x = 0.5
Vertical asymptotes: x = 0.5
Horizontal asymptote: y = 1.5
Sketch:
- There is a vertical asymptote at x = 0.5.
- There is a horizontal asymptote at y = 1.5.
- The function approaches the horizontal asymptote as x approaches positive or negative infinity.