Chapter 7 Rational Functions - College of the Redwoods

656 Chapter 7 Rational Functions
In Exercises 29-36, find the equations
of all vertical asymptotes.
29. f(x) = x2 − 7x
x 2 − 2x
30. f(x) = x2 + 4x − 45
3x + 27
31. f(x) = x2 − 6x + 8
x 2 − 16
32. f(x) = x2 − 11x + 18
2x − x 2
33. f(x) = x2 + x − 12
−4x + 12
34. f(x) = x2 − 3x − 54
9x − x 2
35. f(x) =
16 − x2
x 2 + 7x + 12
36. f(x) = x2 − 11x + 30
−8x + 48
In Exercises 37-42, use a graphing calculator
to determine the behavior of the
given rational function as x approaches
both positive and negative infinity by performing
the following tasks:
i. Load the rational function into the Y=
menu of your calculator.
ii. Use the TABLE feature of your calculator
to determine the value of f(x) for
x = 10, 100, 1000, and 10000. Record
these results on your homework in table
form.
iii. Use the TABLE feature of your calculator
to determine the value of f(x) for
x = −10, −100, −1000, and −10000.
Record these results on your homework
in table form.
iv. Use the results of your tabular exploration
to determine the equation of
the horizontal asymptote.
37. f(x) = (2x + 3)/(x − 8)
38. f(x) = (4 − 3x)/(x + 2)
39. f(x) = (4 − x 2 )/(x 2 + 4x + 3)
40. f(x) = (10 − 2x 2 )/(x 2 − 4)
41. f(x) = (x 2 − 2x − 3)/(2x 2 − 3x − 2)
42. f(x) = (2x 2 − 3x − 5)/(x 2 − x − 6)
In Exercises 43-48, use a purely analytical
method to determine the domain
of the given rational function. Describe
the domain using set-builder notation.
43. f(x) = x2 − 5x − 6
−9x − 9
44. f(x) = x2 + 4x + 3
x 2 − 5x − 6
45. f(x) = x2 + 5x − 24
x 2 − 3x
46. f(x) = x2 − 3x − 4
x 2 − 5x − 6
47. f(x) = x2 − 4x + 3
x − x 2
48. f(x) =
x 2 − 4
x 2 − 9x + 14
Version: Fall 2007