College Algebra Final Review This review should prepare you for the comprehensive final in College Algebra. Read the question, work out the answer, then check yourself by clicking the mouse to see if you’re right.

1. Simplify : 5(2x + 3y)2 - (x -4) + 2(3z-2y) 20x2+45y2+60xy-x-4y+6z+4

2. Solve the following inequality, expressing your final answer in interval notation. -3(2x-1)≤2(3-x) [-3/4,∞)

3. x²-x-6 • x²+7x+12 x²-2x-8 x²-9 X+4 x-4

4. Solve: 4(3x+5)-2(5-2x) = 2x+3 X=-.5

5. Solve: 2x2 + 5x = 3 -3 and 1/2

6. Solve for x: 200 e3x-1=50 -.129

7. Solve for x: 7 log2(x+2)=35 30

Find the slope and y-intercept of 3x + 2y = 3. Then graph. Slope is -3/2 and the y-intercept is 3/2 or 1.5.

9. a)Write the equation of the line containing (1,4) and (3,8) A) Y=2x+2

9b) What is the distance between the two points: (1,4) and (3,8) 9b) What is the distance between the two points: (1,4) and (3,8)? 9c) What is the midpoint of the points above? 9b) 2√5 9c) (2,6)

10. For the following function, determine the axis of symmetry, vertex, direction, x-intercept(s), y-intercept, and graph: y = x²-4x+3 Axis of symmetry is x=2, vertex is (2,-1), direction is up, x-intercepts are 1 and 3, y-intercept is 3

11. Given that f(x)=2x-3 and g(x)=3x²+x-5, determine a) f(7)-f(1) 11. Given that f(x)=2x-3 and g(x)=3x²+x-5, determine a) f(7)-f(1) b) g(2)/f(1) A. 12 B. -9

Find a) (f◦g)(x) b) (g◦f)(x)    

13. Determine the inverse of a) h(x)=x³+2 b) y = 7x + 5

14. Solve each system: a) x + 3y = -2 14. Solve each system: a) x + 3y = -2 y = 3x + 6 b) x + y + z = 2 2x + y –z = 5 x – y + z = -2 a. (-2, 0) b. (1, 2, -1)

15. Factor each of the following completely: a) 4x2 – 13x -35 b) 5x2 – 45 c) 5x2 – 15x + 4xy – 12y B) 5(x+3)(x-3) C) (5x+4y)(x-3)

16. 2x + 3 x²-1 x²-x-2 2x-3 (x-1)(x-2)

17. Perform the indicated operation: (2x4 - 3x3 - 6x2 - 8x - 3) / (x - 3)

18. Simplify: x-2y-1(-2)x-1y-2 xy(-2)3 1___ 4x4y4

19. Solve: x2 - 6x = -7 3+√2 and 3-√2

20. Solve: |y - 8| - 7 = 3 18 or -2

21. Solve 9x-4=275-x X= 23/5 or x=4.6

22. The functions y1=(x-3)5+1 and y2=(x+2)5+5 are graphed on the same axes. Explain how the graph of y2 can be obtained by a translation of y1. Shifted left 5 and up 4.

f(x)= 3_ 23. What is the y-intercept? 1-x 24. What is the x-intercept? 23. Y-intercept is 3 24. there isn’t an x-intercept (To find the y-intercept, set x=0 so you get y= 3/(1-0), which is 3) (To find the x-intercept, set y=0 so you get 0=3/(1-x) This can never equal 0.)

25. Graph y=-3

What is the equation of the line that passes through (1,4) and is perpendicular to y = 2/3 x + 5?

27. Graph the piecewise function: y= -2x if x≤ -1 = 2 if x> -1 Is this a function? What is the domain? What is the range? Yes (-∞, ∞) [2, ∞)

28. Graph y = 2|x+2| - 3 Notice the vertex is at (-2,-3) and the V is skinnier than the parent graph because the slope to the right of the vertex is 2 and the slope to the left of the vertex is -2 (goes up 2, over 1)

29. Where is center? Radius? (x – 7)² + (y + 4)² = 49 Center is (7,-4) Radius is 7 units

30. a) What shape does the equation make. b) Where is the center 30. a) What shape does the equation make? b) Where is the center? What is the length of the major axis? What is the length of the minor axis? (x-2)² + y² = 1 25 9 A) ellipse B) (2,0) C) 10 D) 6

  X= 3 and x = -3

  45

33. Solve the system of equations. x+y=7 x²+y²=25 (4,3) and (3,4)

   

  x= 3, y=2.5 or 5/2, z= -10

THE END Enjoy your summer!