College Algebra, 2013a

4.2 Graphs of Rational Functions 333
4.2.1 Exercises
In Exercises 1 - 16, use the six-step procedure to graph the rational function. Be sure to draw any
asymptotes as dashed lines.
1. f(x) = 4
x +2
2. f(x) = 5x
6 − 2x
3. f(x) = 1 x 2 4. f(x) =
2x − 1
5. f(x) =
−2x 2 − 5x +3
7. f(x) = 4x
x 2 +4
6. f(x) =
1
x 2 + x − 12
x
x 2 + x − 12
8. f(x) = 4x
x 2 − 4
9. f(x) = x2 − x − 12
x 2 + x − 6
11. f(x) = x2 − x − 6
x +1
13. f(x) = x3 +2x 2 + x
x 2 − x − 2
15. f(x) = x3 − 2x 2 +3x
2x 2 +2
10. f(x) = 3x2 − 5x − 2
x 2 − 9
12. f(x) = x2 − x
3 − x
14. f(x) = −x3 +4x
x 2 − 9
16. 18 f(x) = x2 − 2x +1
x 3 + x 2 − 2x
In Exercises 17 - 20, graph the rational function by applying transformations to the graph of y = 1 x .
17. f(x) = 1
x − 2
19. h(x) =
−2x +1
x
18. g(x) =1− 3 x
(Hint: Divide) 20. j(x) = 3x − 7
x − 2
(Hint: Divide)
21. Discuss with your classmates how you would graph f(x) = ax + b . What restrictions must
cx + d
be placed on a, b, c and d so that the graph is indeed a transformation of y = 1 x ?
22. In Example 3.1.1 in Section 3.1 we showed that p(x) = 4x+x3
x
is not a polynomial even though
its formula reduced to 4 + x 2 for x ≠ 0. However, it is a rational function similar to those
studied in the section. With the help of your classmates, graph p(x).
18 Once you’ve done the six-step procedure, use your calculator to graph this function on the viewing window
[0, 12] × [0, 0.25]. What do you see?