For each function, identify the points of discontinuity, holes, intercepts, horizontal asymptote, vertical asymptote(s) and domain. Then sketch the graph.
Consider the rational functions on the right.
Use the items on the left to identify each function's:
◆ Domain
◆ Points of discontinuity (and the type of discontinuity each represents: removable or non-removable)
◆ x- and y- intercepts
domain: all real numbers
domain: all real numbers except x = ±4
domain: all real numbers except x = -2, -1
no points of discontinuity
non-removable discontinuity at x = ±4
removable discontinuity at x = -2
non-removable discontinuity at x = -2
removable discontinuity at x = -1
no x-intercept
x-intercept: (1, 0)
x-intercept: (-1, 0)
y-intercept: (0, -1/16)
y-intercept: (0, 1/2)
y-intercept: (0, -1/3)
Answer Key for #3
Discontinutities at x=3 and x=-3
Holes: None
Horizontal Asymptote: y=1
Vertical Asymptotes: x=3 and x=-3
X-Intercepts: (2,0) and (-2,0)
Y-Intercept: (0, 4/9)
Domain: All reals except -3 and 3
