Download Assignment #1 - Algebra Review

Math 111
Connolly
Assignment #1 - Algebra Review
Complete each of the following. Show all important steps and please clearly indicate your final answer.
All work should be in appropriate mathematical form and use appropriate mathematical notation.
The work completed on this worksheet should be your work and yours alone. You may refer to outside
books for assistance on any topics that are covered. You may go to The Math Center for general help on
concepts, but not for the specific problems assigned on this sheet.
This assignment is due at the beginning of class on Friday, July 10, 2009. It will not be accepted late.
Please staple all pages together and sign and date a pledge statement for the assignment.
1. If f(x) = 2x2 – 3x + 4 find f(2), f(-1), f(a) and f(x+h)
2. If f(x) = 3x – 5 and g(x) = x2 + 2 find f(g(x)) and g(f(x))
3. Factor 2x2 – 5x – 3
4. Factor 25x2 – 4
5. Factor 3x3 – 4x2 - 4x
6. Factor 2x2 + 9xy – 5y2
7. Add
2
1
a 1
  2
a  2 a a  2a
8. Multiply and simplify
y 2  2 y 3y  3

6 y  12 15 y  30
9. Solve for x : 7x + 4 = 16 – 3x
10. Solve for x : 6x2 – x – 2 = 0
11. Solve for x : 3x2 – 2x + 1 = 2
12. Solve for r : 6r2 + 7r = 3
13. Solve for t : t2 + 1 = 4t
14. Solve for z :
3
 12  0
z2
15. Solve for y : 3y2 + 5y = 0
16. Solve for s : 4 – 3s < 7 + 2s
17. Solve for r : r2 + 3r > 4
18. Solve for x : 2 x  5  7
19. Write the equation of the line that passes through the points (3,5) and ( -1,2)
20. Write the equation of the line that passes through the point (-2,6) and is perpendicular to 2x - 3y = 5
21. Write the equation of the line with x-intercept 4 that is parallel to x + 2y = 7
22. A company finds that it can make a total of 20 solar heaters for $13900, while 10 solar heaters cost
$7500 to make. Write a linear function to represent the total cost, y, of producing x solar heaters.
23. An artist sells silk-screened t-shirts at community festivals and crafts fairs. Her variable cost to
produce one t-shirt is $3.50. Her total cost to produce 60 t-shirts is $300. She sells the shirts for $9
each. Find a linear function to represent the total cost, C(x), of making x shirts. How many t-shirts
must she produce and sell in order to make a profit of $500.
24. Sketch the graph of f(x) = 2x-5
25. Sketch the graph of f(x) = x2 –3
26. Sketch the graph of g(x) = -x2 +4
27. Sketch the graph of h(x) = x  1
28. Sketch the graph of k(x) = x  1
29. At what point(s) would the graph of f(x) = x2 – 3x cross the x-axis?
30. At what point(s) would the graph of f(x) = x2 – 3x – 4 cross the x-axis? The y-axis?
31. At what point(s) would you expect the graphs of f(x) = 3x3 – x2 – 10x and g(x) = -x2 + 2x intersect?
32. Using the graph below, find f(1), f(-6), f(4), f(-2) and f(7). State the domain and range of y = f(x).
33. Simplify : 3x 2 (2 x 2 ) 3
 3y 
34. Simplify :  
 4x 
3
 2x 
 
 y 
1
3
1
35. Simplify : (27 x 4 ) 3 (4 x 3 ) 2
These problems are from Calculus, 4th edition, by Stewart, Calculus with Applications, 6th edition, by Lial, Greenwell & Miller,
and Brief Calculus, an Applied Worktext, by Larson and Edwards.