Luttrell 2012
140
Name: ______________________
Date: _____
7 - Rational Functions
Expand these polynomials:
1. (6
x
+ 5)
2
2. (
x
-
y
)
3
3. (2
x
+ 4)
2
Factor these polynomials:
4.
x
2
- 6
x
- 27
5. 12
x
2
+ 25
x
+ 12
6. 7
a
4
- 28
b
2
7. 9
x
2
- 4
y
6
8. 8
x
3
- 27
y
12
9. 4
xy
-3
y
-8
xy
2
+ 6
y
2
Simplify these rational expressions:
10.
x
xy
y
x
y
y
x
y
x
2
2
2
2
2
+
+
−
÷
+
−
11.
1
1
4
1
2
1
−
−
+
−
x
x
12.
x
x
x
x
x
+
−
+
+
+ +
2
1
1
1
3
2
Solve these equations:
13. 2
x
2
- 5
x
= 7
14.
x
x
x
x
+
−
=
−
3
2
3
18
4
9
2
15.
2
1
3
1
5
x
x
+
−
−
=
16. A rectangular piece of cardboard has area of 200 cm
2
. The length is four times its width.
Find the dimensions of the cardboard.
17. A metal worker wants to make sure an open box made from 6" by 8" sheet of metal has
maximum volume. The box was made by cutting out equal squares from the corners of the
sheet and then bending edges. Once you determine the equation to represent volume, use
a calculator to find the maximum volume and corresponding dimensions of the box. Explain
how you got your answer.
Reduce the equations. Graph, labelling the intercepts and discontinuities. Differentiate between
removable and nonremovable asymptotes. No calculator!
18.
f x
x
x
x
x
( )
(
)(
)
=
− −
+
+
2
2
6
2
3
19.
f x
x
x
( )
=
+
+
3
3
1
3
