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Topic 8 - Graphing Rational Functions HW 4

Last updated almost 5 years ago
3 questions
20

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)
10
1

For each function, identify the points of discontinuity, holes, intercepts, horizontal asymptote, vertical asymptote(s) and domain. Then sketch the graph.

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