Math 99-BN
Review Activity #6
Satake
1. Find the domain and range of the relations below. Indicate whether the relation represents a function. Explain.

1
3



b.  3, 1 ,  2,0 ,  0, 1,  ,0.7 ,  3,7  
a.

x
y
0
3
-2
1
5
10
-7
1
-2
8
5
1

2. Determine whether the relations below are functions. Explain. Then find the domain and range of the relations below.
Use interval notation where appropriate. Each tick mark represents 1 unit.
a.
b.
(-4,2)
(3,2)
(0,1)
(-2,0)
(2,0)
(0,-2)
c.
d.
Left endpoints of each segment are open.
3. Use the graph at right to answer the following questions.
a. Find the domain and range, and write using interval notation.
b. f  3   ?
c. For what value(s) of x does f  x   2?
4. Find the domain for the following functions. Write the domain using interval notation.
a. f  x  
x4
 2x  1 x  3 
c. p  x   x 2  8x  15
b. g  x   3 x  4
5. Consider the functions f  x   5x  9, g  x   3x 2  x  8, h  x   3, and k  x   x  4 . Find the following.
a. f  3 
b. f  x  1
c. g  2 
e. h  4 
f. k  7 
g. k  0 
d. g  0 
6. Graph the following functions using at least 5 points. Label your points on the graph. For b, c, and d, find the x and y
intercepts.
a. f  x  
c. h  x  
1
x 3
b. g  x   x  4  2
d. q  x   2  x  1  3
2
x 2
Perform the indicated operations and simplify.
2x 3  16
7.
8  2x  3 x 2
10.
8.
2p  3
2
2p  7 p  6
2x 2  5 xy  2y 2 x 2  xy  2y 2
 2
4x 2  y 2
2x  xy  y 2
9.
11.
x  5y y 2  x 2

x 2  xy 10y  2x
x
5
 2
x  3 x  10 x  3 x  10
2
1
12. Simplify:
y 3
4

y
y 1
13. Simplify:
y
1

y 1 y
1
x y
x 2  y 2
Solve the following equations.
14.
2
1
6
 
3x  1 x 3x  1
16. Solve for x: y 
15.
xz
ax
3
21
14
 2

x 2 x 4 x 2
17. Solve for (lower case) v:
PV pv

T
t
18. Assume the two right triangles are similar. Set up a rational equation to find the missing sides and solve. Round to
the nearest hundredth. You may need to use the Pythagorean Theorem.
12.5 m
c
2.8 m
8m
b
x
19. Evaluate: 216
2
 64 
20. Evaluate: 

 125 
3
2
3
Simplify the following radicals. Assume all variables represent positive real numbers.
21.
3
64x 14 y 9 z 3
22.
200a16b9c 2d
23.
4
y 17
625
Perform the indicated operations. Assume all variables represent positive real numbers, where appropriate.
24. 6q 2 3 5q  2q 3 40q 4
26. 9 27 p 2  14 108 p 2  2 p 48
25. 3 7z  9 3 7z
27. 3 2

32  2 9


28. 4 3 xy 3
 2
6x3y 2

29.

x 3 y
9
x y



30. 5  2 5  2

Solve the following application problems. Be sure to define your variable, set up your equation and solve.
31. A Hudson River tugboat goes 10 mph in still water. It travels 24 mi upstream and 24 mi back in a total time of 5
hours. What is the speed of the current?
32. A new printing press prints the morning edition in 8 hours, whereas the old printer took 12 hours. How long would it
take to print the morning edition if both printers were working together?