Module 1. Name: Date: Period: Find the following function values. 4. Find the following: Domain. Range. The graph is increasing over the interval

Transcription

1 Name: Date: Period: Algebra Fall Final Exam Review My Exam Date Is : Module 1 Find the following function values. f(x) = 3x + g(x) = x h(x) = x 3 1. g(f(x)). h(3) g(3) 3. g(f()) 4. Find the following: As, x f( x) As x, f( x) Domain Range The graph is increasing over the interval The graph is decreasing over the interval 5. Find the following: As, x f( x) As x, f( x) Domain Range The graph is increasing over the interval The graph is decreasing over the interval

2 Match how the following graphs are obtained from the graph of y = f(x) 6. y = f(x + 4) A. horizontal stretch B. horizontal compression 7. y = 4f(x) C. translate 4 units up D. translate 4 units down 8. y = f(-x) E. reflection over the y axis F. reflection over the x-axis 9. y = f(x) + 4 G. vertical compression H. vertical stretch 10. y = f(4x) 11. y = 1 4 f(x) I. translate 4 units to the right J. translate 4 units to the left Draw the graph of the function with its given domain. Then determine the range using interval notation. 1. f(x) = x + with domain:(, 3) 13. f(x) = x 3 with domain: [-3, 6) 3 Range: Range:

3 14. Use the graph of g(x) below to complete the transformation y = g(x) 15. Use the graph of g(x) below to complete the transformation y = g(x) 16. f(x) = 3x f (x) = Proof they are inverses: f f x f f x 1 1 ( ( )) and ( ( ))

4 Complete each domain with the given notation: 17. Inequality: x 5 Set Notation: Interval Notation: 18. Inequality: Set Notation: Interval Notation: (-, ] 19. Inequality: Set Notation: {x x > 3} Interval Notation: 0. Inequality: Set Notation: Interval Notation: [-, 4) Module 1. List all the transformations for the following absolute values: 1 a) f(x) 3 x 7 b) f(x) x 4 3. The minimum point on the graph of the equation y = f(x) is (5,- ). What is the minimum point on the graph of the equation y = f(x + ) - 4 Solve the following absolute value equations: 3. A) 3 4w B) w Solve the following absolute value inequalities. Write your answer in interval notation A) c B) x 6 7 5

5 5. Write the equation of the absolute value: A) B) 6. If your oven is set to 350 degrees, but you know that it varies by 5 degrees. What absolute value inequality could you use to find the coolest and warmest temperatures your oven can be? 7. A road must be 40 feet wide, but they are allowed a tolerance of 18 inches. What absolute value inequality could you use to find the widest and narrowest the road can be? Solve the absolute value equation by graphing A) x B) x What is the solution to the following graph?

6 Module 3 I. Graph then find the following attributes y ( x 3) 4. y ( x ) 5 3. y ( x 3) 1 D: R: D: R: D: R: Axis Of Symmetry: Axis Of Symmetry: Axis Of Symmetry: Min/Max: Min/Max: Min/Max: Increasing: Increasing: Increasing: Decreasing: Decreasing: Decreasing: 1 4. y 4( x ) 3 5. y ( x 4) 5 6. y ( x ) 5 D: R: D: R: D: R: Axis Of Symmetry: Axis Of Symmetry: Axis Of Symmetry: Min/Max: Min/Max: Min/Max: Increasing: Increasing: Increasing: Decreasing: Decreasing: Decreasing:

7 II. Write the quadratics in vertex form by completing the square. 7. y x 16x 4 8. y x 4x 3 9. y 3x 6x f(x) x x 3 III. Use the information in the graph to write the equation of the parabola in vertex form IV. Write the equation of the parabola in vertex form given the following information. 14. Vertex: (4,1), opens up, Point (,) 15. Vertex: (-,3), opens down, Point (-4,-9) 16. Points (3,-4) and (-,-14) and has an axis of symmetry of x = 1

8 17. Use the projectile motion model: h(t) = -16t + v ot + h o and your Nspire to answer the following questions. Tammy tosses a coin off a bridge into the stream below. She throws the coin with an initial upward velocity of 64 feet per second off the bridge 19 feet above the stream. a. Write the quadratic equations that models this situation: b. Sketch the graph that models this situation. c. How long did it take to reach the maximum height? d. What is the maximum height of the coin? e. How long will it take the coin to hit the water? f. How long was the coin descending? Module 4 Simplify each expression. Write your answer in a + bi form i 4. (5 3i) (- + 8i) 5. 5 i 4 3i 6.

9 Solve by Factoring. 7. x = 1x 8. x + 10x = x = -9x x 14x 3 0 Solve by the square root method. 11. x x x 5 Solve by completing the square. 14. x 4x x 4x 8 0

10 Solve by quadratic formula x 4x x 6x 11 0 Give the value of the discriminant and describe the nature of the roots n = 4n x - 8x = -4 Solve by graphing. 1 x x x 1 4

11 Module 5 1. Solve the system by substitution.. Solve the system by elimination. x y 35 x 4y 0 3x 4y 8 x y 6 3. Solve using a matrix 3b c 15 a 3b c 11 3a 4b c Steve is cashing in his jar of spare nickels, dimes, and quarters. When he gets to the bank, he receives a total of $ He learns that he had 133 coins in all, and that there were 3 times as many dimes as quarters. How many of each type of coin did he save? a. Write a system of equations that models this situation. b. Solve the system using any method. How many of each type of coin did Steve save?

12 Solve this system using matrices. 5. 3r s t 15r 6s 9t 4 1r 15t 4 6. Solve the following system of equations y x 7 x 5 y x 3 7. Conner invested $10,000 for one year in three different investments. The investments paid simple interest of 3%, 8%, and 15%, respectively, and he received a total of $500 in interest for the year. He invested $3000 more at 3% than 8%. a. Write the system of equations for this problem b. Find the amount invested at each rate.

13 Using a graphing calculator, answer the following questions. Answers should be in FRACTION form A= B= C= D= A - B 9. CB 10. BD 11. 5A 1. What are the solutions for the linear-quadratic system below?