Algebra II Chapter 3 Test Review Standards/Goals: F.IF.1:

Transcription

1 1 Algebra II Chapter 3 Test Review Standards/Goals: F.IF.1: o o I can understand what a relation and a function is. I can understand that a function assigns to each element of a domain, EXACTLY one element of the range. F.IF.2.: I can evaluate functions for input values in their domains. F.IF.5.: I can relate the domain of a function to its graph. C.1.d./F.BF.1b.: o o I can perform operations on functions, including: addition, subtraction, multiplication and division. I can determine the domain and range of functions. F.1.a./A.APR.1.: I can evaluate and simplify polynomial expressions and equations. F.BF.3: I can identify the effect on the graph of a function when I replace f(x) with: f(x) + k; k f(x); f(k x); f(x + k) #1. Determine the vertex for the following functions: a. y = 1 x b. y = 4 x c. y= x 7 4 #2. Consider the function: y = 1 x How would it appear, if you reflected it across the y- 4 axis, and shifted it 2 units left and 3 units down? What would its new vertex be? #3. Consider the function: y = 4 x How would it appear, based on the following transformations? What would its new vertex be in each instance? a. f(x 8) 8 b. f(x + 3) + 4 c. f(x 17) 3 d. 2f(x 6) #4. Be able to distinguish the effect of the graph of the parent function: y = x i. y = 3 x ii. y = 3 x iii. y = -1/3 x iv. y = 1/3 x #5. Consider the relation: {(9, 3), (3, 7), (-3, 0), (-5, 3)} Write the resulting relation, after translating it 4 units to the RIGHT.

2 2 #6. Consider the following: y = f(x). Write an equation of a new graph, if the following occur. a. Reflected in the x-axis, translated/shifted 4 units left and translated/shifted up 6 units. b. Reflected in the x-axis, translated/shifted 6 units right and translated/shifted down 10 units. c. Reflected in the y-axis, translated/shifted 10 units left and translated/shifted down 8 units and stretched by a factor of 4. d. Reflected in the x AND y axis and compressed by a factor of ½ and shifted down 12 units. #7. Find the domain of each of the following: a. f(x) = 5 b. f(x) = x + 6 c. f(x) = 7 x 9 x 10 #8. The domains for each of the following are both D: (, ). Explain why that is the case. f(x) = 6x 9 f(x) = 5x 2 + 6x 10 Consider the functions: f(x) = x and g(x) = 3x 5 #9. Find f(g(x)) and g(f(x)) #10. Find f(-5) + g(5) #11. Find f(x 1) #12. Find g(x + 8) + f(-8). Consider the following functions: f(x) = 4x + 8 g(x) = x h(x) = x + 7 m(x) = 6x 10 #13. Find f(1/2) #14. Find g(-9) #15. Find h(18) #16. Find m(-0.5)

3 3 #17. Consider the following function: g(x) = 1 x a. Identify the more basic, parent function that has been shifted, reflected, Answer: y = b. Indicate how the basic function found in step 1 has been shifted, reflected, Horizontal shift: ᴑ LEFT ᴑ RIGHT ᴑ NONE Stretch/Compress: ᴑ STRETCH ᴑ COMPRESS ᴑ NONE By a factor of: X-Axis Reflection: Y-Axis Reflection: Vertical Shift: ᴑ UP ᴑ DOWN ᴑ NONE #18. Consider the following function: g(x) = x 4 7 a. Identify the more basic, parent function that has been shifted, reflected, Answer: y = b. Indicate how the basic function found in step 1 has been shifted, reflected, Horizontal shift: ᴑ LEFT ᴑ RIGHT ᴑ NONE Stretch/Compress: ᴑ STRETCH ᴑ COMPRESS ᴑ NONE By a factor of: X-Axis Reflection: Y-Axis Reflection: Vertical Shift: ᴑ UP ᴑ DOWN ᴑ NONE

4 4 #19. Consider the following function: g(x) = 6(x 4) a. Identify the more basic, parent function that has been shifted, reflected, Answer: y = b. Indicate how the basic function found in step 1 has been shifted, reflected, Horizontal shift: ᴑ LEFT ᴑ RIGHT ᴑ NONE Stretch/Compress: ᴑ STRETCH ᴑ COMPRESS ᴑ NONE By a factor of: X-Axis Reflection: Y-Axis Reflection: Vertical Shift: ᴑ UP ᴑ DOWN ᴑ NONE #20. Consider the following function: g(x) = 5 x a. Identify the more basic, parent function that has been shifted, reflected, Answer: y = b. Indicate how the basic function found in step 1 has been shifted, reflected, Horizontal shift: ᴑ LEFT ᴑ RIGHT ᴑ NONE Stretch/Compress: ᴑ STRETCH ᴑ COMPRESS ᴑ NONE By a factor of: X-Axis Reflection: Y-Axis Reflection: Vertical Shift: ᴑ UP ᴑ DOWN ᴑ NONE

5 5 #21. Using the graph of the relation below, answer the following: #22. Using the graph of the relation below, answer the following: #23. Using the graph of the relation below, answer the following:

6 6 #24. Using the graph of the relation below, answer the following: #25. Using the graph of the relation below, answer the following: #26. Using the graph of the relation below, answer the following:

7 7 FLASHBACK SECTION: Solve each inequality, graph the solution and write an interval for its solution. #1. -10x > 70 #2. -2x 10 < 26 #3. 4 < 2x 2 18 #4. 2x #5. -2 x > 22 # x + 9 < 8 #7. 4 8x 9 > 20 #8. x = 17

8 8 # x 12 = 7 #10. 2 x 10 #11. 2 x 10 #12. What is the equation, in standard form, of the line that passes through (-6, -8) and has a slope of 3? #13. What is the equation, in standard form, of the line that passes through (10, -6) and has a slope of ½? #14. What is the equation, in standard form, of the line that passes through (8, -2) and has a slope of 8?