GRAPHING RATIONAL FUNCTIONS WORKSHEET
Identify the points of discontinuity, holes, vertical asymptotes, x – intercepts, horizontal asymptote, and domain of each. Then sketch the graph.
1) f(x) = (x + 1)/(x – 2)
2) f(x) = (x2 + 2x – 8)/(-x2 + 6x – 8)
3) f(x) = (x2 - 7x + 12)/(-2x2 - 2x + 24)
4) f(x) = (3x2 - 3x - 18)/(x2 - 4)
5) f(x) = (x2 + 6x + 8)/(x2 + 3x - 4)
6) f(x) = (2x + 6)/(x2 + 5x + 6)
7) f(x) = (-2x - 6)/x
8) f(x) = (-3x + 12)/(x – 2)
9) f(x) = -3/x
10) f(x) = (x3 + x2 – 12x)/(x3 – x2 – 6x)
Answer Key
1) discontinuous at x = 2.
No hole.
Vertical asymptote at x = 2
x – intercepts is -1.
Horizontal asymptote is y = 1
All real values except 2
2) Discontinuous at x = 2 and x = 4.
Hole at x = 2.
Vertical asymptote at x = 4.
x – intercepts is -4.
Horizontal asymptote is y = -1.
All real values except 2 and 4.
3) Discontinuous at x = 3 and x = -4.
Hole at x = 3.
Vertical asymptote at x = -4.
x – intercepts is 4.
Horizontal asymptote is y = -1/2.
All real values except 3 and -4.
4) discontinuous at x = 2 and x = -2.
Hole at x = -2.
Vertical asymptotes at x = 2.
x – intercepts is 3.
Horizontal asymptote is y = 3.
All real values except -2 and 2.
5) Discontinuous at x = -4 and x = 1.
Hole at x = -4.
Vertical asymptotes at x = 1.
x – intercepts is -2.
Horizontal asymptote is y = 1.
All real values except -4 and 1
6) Discontinuous at x = -2 and x = -3.
Hole at x = -3.
Vertical asymptotes at x = -2.
x – intercepts is none.
Horizontal asymptote is y = 0
All real values except -3 and -2.
7) Discontinuous at x = 0.
No hole
Vertical asymptotes at x = 0.
x – intercepts is -3.
Horizontal asymptote is y = -2.
All real values except 0
8) discontinuous at x = 2.
No hole
vertical asymptote at x = 2.
x – intercepts is 4.
horizontal asymptote is y = -3.
all real values except 2
9)
Discontinuous at x = 0.
No hole
vertical asymptotes at x = 0.
No x – intercept.
Horizontal asymptote is y = 0
All real values except 0.
10)
Discontinuous at x = 0, x = -2 and x = 3.
Holes are at x = 0, x = 3.
Vertical asymptote at x = -2.
x – intercepts is -4.
Horizontal asymptote is y = 1.
All real values except 0, -2 and 3.
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