Algebra 2 2



Algebra 2 2.5-2.7 Review

Multiple Choice

Identify the choice that best completes the statement or answers the question.

Graph each equation by translating y = | x |.

____ 1. y = | x + 5 | + 2

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 2. y = | x + 2 |

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

Write an equation for each translation of [pic].

____ 3. 7 units up

|a. |y + 7 = | x | |c. |y = | x | – 7 |

|b. |y = | 7x | |d. |y = | x | + 7 |

____ 4. 13 units left

|a. |y = | x | – 13 |b. |y = | x + 13 | |c. |y = | x | + 13 |d. |y = | x – 13 | |

____ 5. 15.5 units down

|a. |y – 15.5 = | x | |c. |y = | x | – 15.5 |

|b. |y = | x | + 15.5 |d. |y = | –15.5x | |

Graph the absolute value equation.

____ 6. [pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 7. Write an equation for the horizontal translation of [pic].

[pic]

|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |

____ 8. Graph y = | x | – 3.

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

Find the value of y for a given value of x, if y varies directly with x.

____ 9. If y = 67 when x = 402, what is y when x = 432?

|a. |–2592 |b. |2592 |c. |72 |d. |–72 |

____ 10. If y = 3.6 when x = –0.36, what is y when x = –0.17?

|a. |1.7 |b. |–0.02 |c. |–1.7 |d. |0.02 |

Determine whether y varies directly with x. If so, find the constant of variation k.

____ 11. 4y = –x

|a. |yes; [pic] |b. |yes; [pic] |c. |yes; –1 |d. |no |

____ 12. –3y = 2x + 21

|a. |yes; 2 |b. |no |c. |yes; –3 |d. |yes; [pic] |

____ 13. The graph models a train’s distance from a river as the train travels at a constant speed. Which equation best represents the relation?

[pic]

|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |

____ 14. Graph the function [pic].

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 15. The equation [pic] describes a function that is translated from a parent function.

|a. |Write the equation of the parent function. Then find the number of units and the direction of translation. |

|b. |Sketch the graphs of the two functions. |

|a. |[pic]; 3 units down; |c. |[pic]; 3 units up; |

| |[pic] | |[pic] |

|b. |[pic]; 3 units down; |d. |[pic]; 3 units up; |

| |[pic] | |[pic] |

____ 16. What is the vertex of the function [pic]?

|a. |([pic], –4) |b. |([pic], –4) |c. |([pic], 4) |d. |([pic], 4) |

Write an equation for the vertical translation.

____ 17. [pic]; 9 units down

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 18. Write the equation for the translation of [pic].

[pic]

|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |

____ 19. Describe how the graph is like the graph of y = | x | and how it is different.

[pic]

|a. |The graph is the same as y = | x |. |

|b. |The graphs are the same shape. The y-intercept of y = | x | is 0 and the y-intercept of the second graph is –9. |

|c. |The graphs have the same y-intercept. The second graph is steeper than y = | x |. |

|d. |The graphs are the same shape. The y-intercept of y = | x | is 0 and the x-intercept of the second graph is –9. |

____ 20. Which graph shows the best trend line for the following data.

[pic]

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 21. Write the equation that is the translation of [pic] left 10 units and down 6 units.

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 22. The equation [pic] describes a function that is translated from a parent function.

|a. |Write the equation of the parent function. |

|b. |Find the number of units and the direction of translation. |

|c. |Sketch the graphs of the two functions. |

|a. |[pic]; 2 units left; |c. |[pic]; 2 units right; |

| |[pic] | |[pic] |

|b. |[pic]; 2 units left; |d. |[pic]; 2 units right; |

| |[pic] | |[pic] |

____ 23. Graph the function [pic].

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 24. Graph the equation of y = |x| translated 5 units down.

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

Algebra 2 2.5-2.7 Review

Answer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1 DIF: L3

REF: 6-8 Graphing Absolute Value Equations

OBJ: 6-8.1 Translating Graphs of Absolute Value Equations NAT: NAEP 2005 A2d | ADP K.6

STA: MS A1.3 KEY: translation | absolute value

2. ANS: C PTS: 1 DIF: L2

REF: 6-8 Graphing Absolute Value Equations

OBJ: 6-8.1 Translating Graphs of Absolute Value Equations NAT: NAEP 2005 A2d | ADP K.6

STA: MS A1.3 TOP: 6-8 Example 4

KEY: translation | absolute value | graphing equations

3. ANS: D PTS: 1 DIF: L2

REF: 6-8 Graphing Absolute Value Equations

OBJ: 6-8.1 Translating Graphs of Absolute Value Equations NAT: NAEP 2005 A2d | ADP K.6

STA: MS A1.3 TOP: 6-8 Example 3

KEY: absolute value | translation | graphing

4. ANS: B PTS: 1 DIF: L2

REF: 6-8 Graphing Absolute Value Equations

OBJ: 6-8.1 Translating Graphs of Absolute Value Equations NAT: NAEP 2005 A2d | ADP K.6

STA: MS A1.3 TOP: 6-8 Example 5 KEY: absolute value | translation

5. ANS: C PTS: 1 DIF: L3

REF: 6-8 Graphing Absolute Value Equations

OBJ: 6-8.1 Translating Graphs of Absolute Value Equations NAT: NAEP 2005 A2d | ADP K.6

STA: MS A1.3 TOP: 6-8 Example 3

KEY: absolute value | translation | graphing

6. ANS: B PTS: 1 DIF: L2

REF: 2-5 Absolute Value Functions and Graphs

OBJ: 2-5.1 Graphing Absolute Value Functions STA: MS AII 4b

TOP: 2-5 Example 1 KEY: absolute value

7. ANS: D PTS: 1 DIF: L2 REF: 2-6 Families of Functions

OBJ: 2-6.1 Translating Graphs TOP: 2-6 Example 2

KEY: horizontal translation

8. ANS: D PTS: 1 DIF: L2

REF: 6-8 Graphing Absolute Value Equations

OBJ: 6-8.1 Translating Graphs of Absolute Value Equations NAT: NAEP 2005 A2d | ADP K.6

STA: MS A1.3 TOP: 6-8 Example 2

KEY: absolute value | translation | graphing

9. ANS: C PTS: 1 DIF: L2 REF: 2-3 Direct Variation

OBJ: 2-3.1 Writing and Interpreting a Direct Variation STA: MS AII 5c

TOP: 2-3 Example 4 KEY: direct variation

10. ANS: A PTS: 1 DIF: L2 REF: 2-3 Direct Variation

OBJ: 2-3.1 Writing and Interpreting a Direct Variation STA: MS AII 5c

TOP: 2-3 Example 4 KEY: direct variation

11. ANS: A PTS: 1 DIF: L2 REF: 2-3 Direct Variation

OBJ: 2-3.1 Writing and Interpreting a Direct Variation STA: MS AII 5c

TOP: 2-3 Example 2 KEY: constant of variation

12. ANS: B PTS: 1 DIF: L2 REF: 2-3 Direct Variation

OBJ: 2-3.1 Writing and Interpreting a Direct Variation STA: MS AII 5c

TOP: 2-3 Example 2 KEY: constant of variation

13. ANS: C PTS: 1 DIF: L3

REF: 2-5 Absolute Value Functions and Graphs

OBJ: 2-5.1 Graphing Absolute Value Functions STA: MS AII 4b

TOP: 2-5 Example 4 KEY: constant speed | relation | absolute value

14. ANS: B PTS: 1 DIF: L2 REF: 2-6 Families of Functions

OBJ: 2-6.1 Translating Graphs TOP: 2-6 Example 2

KEY: horizontal translation

15. ANS: D PTS: 1 DIF: L2 REF: 2-6 Families of Functions

OBJ: 2-6.1 Translating Graphs TOP: 2-6 Example 1

KEY: vertical translation | multi-part question

16. ANS: C PTS: 1 DIF: L3

REF: 2-5 Absolute Value Functions and Graphs

OBJ: 2-5.1 Graphing Absolute Value Functions STA: MS AII 4b

TOP: 2-5 Example 1 KEY: absolute value | vertex

17. ANS: D PTS: 1 DIF: L3 REF: 2-6 Families of Functions

OBJ: 2-6.1 Translating Graphs TOP: 2-6 Example 1

KEY: vertical translation

18. ANS: D PTS: 1 DIF: L2 REF: 2-6 Families of Functions

OBJ: 2-6.1 Translating Graphs TOP: 2-6 Example 1

KEY: horizontal translation | vertical translation

19. ANS: B PTS: 1 DIF: L2

REF: 6-8 Graphing Absolute Value Equations

OBJ: 6-8.1 Translating Graphs of Absolute Value Equations NAT: NAEP 2005 A2d | ADP K.6

STA: MS A1.3 TOP: 6-8 Example 1 KEY: absolute value | translation

20. ANS: B PTS: 1 DIF: L2

REF: 6-7 Scatter Plots and Equations of Lines

OBJ: 6-7.1 Writing an Equation for a Trend Line

NAT: NAEP 2005 D2e | NAEP 2005 D2g | NAEP 2005 A2c | NAEP 2005 A2f | ADP I.4.2 | ADP J.4.8 | ADP K.10.2 | ADP L.1.1 | ADP L.1.2 | ADP L.1.5 | ADP L.3.4 STA: MS A1.8.a

TOP: 6-7 Example 1 KEY: scatter plot | graphing | data analysis | trend line

21. ANS: D PTS: 1 DIF: L2 REF: 2-6 Families of Functions

OBJ: 2-6.1 Translating Graphs TOP: 2-6 Example 2

KEY: horizontal translation

22. ANS: A PTS: 1 DIF: L2 REF: 2-6 Families of Functions

OBJ: 2-6.1 Translating Graphs TOP: 2-6 Example 3

KEY: horizontal translation | multi-part question

23. ANS: A PTS: 1 DIF: L2 REF: 2-6 Families of Functions

OBJ: 2-6.2 Stretches | Shrinks | and Reflections TOP: 2-6 Example 4

KEY: stretch and shrink

24. ANS: B PTS: 1 DIF: L3 REF: 2-6 Families of Functions

OBJ: 2-6.1 Translating Graphs TOP: 2-6 Example 1

KEY: vertical translation

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