Chapter 7 Rational Functions - College of the Redwoods

Section 7.1 Introducing Rational Functions 615
7.1 Exercises
In Exercises 1-14, perform each of the
following tasks for the given rational function.
i. Set up a coordinate system on a sheet
of graph paper. Label and scale each
axis.
ii. Use geometric transformations as in
Examples 10, 12, and 13 to draw the
graphs of each of the following rational
functions. Draw the vertical
and horizontal asymptotes as dashed
lines and label each with its equation.
You may use your calculator to
check your solution, but you should
be able to draw the rational function
without the use of a calculator.
iii. Use set-builder notation to describe
the domain and range of the given
rational function.
1. f(x) = −2/x
2. f(x) = 3/x
3. f(x) = 1/(x − 4)
4. f(x) = 1/(x + 3)
5. f(x) = 2/(x − 5)
6. f(x) = −3/(x + 6)
7. f(x) = 1/x − 2
8. f(x) = −1/x + 4
9. f(x) = −2/x − 5
10. f(x) = 3/x − 5
11. f(x) = 1/(x − 2) − 3
12. f(x) = −1/(x + 1) + 5
13. f(x) = −2/(x − 3) − 4
14. f(x) = 3/(x + 5) − 2
In Exercises 15-22, find all vertical asymptotes,
if any, of the graph of the given
function.
15. f(x) = − 5
x + 1 − 3
16. f(x) = 6
x + 8 + 2
17. f(x) = − 9
x + 2 − 6
18. f(x) = − 8
x − 4 − 5
19. f(x) = 2
x + 5 + 1
20. f(x) = − 3
x + 9 + 2
21. f(x) = 7
x + 8 − 9
22. f(x) = 6
x − 5 − 8
In Exercises 23-30, find all horizontal
asymptotes, if any, of the graph of the
given function.
23. f(x) = 5
x + 7 + 9
24. f(x) = − 8
x + 7 − 4
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Version: Fall 2007