Algebra 2: Chapter 2 Review Name:

Algebra 2: Chapter 2 Review

Davis

Name: ______________________________________________ Section 1: Relations, Functions, Domain, and Range Identify the domain and range of each relation, state whether the relation is a function, and explain your reasoning.(4 pts) 1. (4, 7);(-3, -5);(3, 7);(4, 4);(2, 6) Domain: ___________________ Range:

___________________

Function?: _____________ Why or why not?: 4. Domain: ___________________ 2. (5, 1);(-2, -3);(5, 1);(6, -2);(2, 7) Range:

___________________

Domain: ___________________ Range:

Function?: _____________ Why or why not?:

___________________

Function?: _____________ Why or why not?:

3. (4, 1);(-2, 1);(-3, 1);(6, -2);(5, 7) Domain: ___________________ Range:

___________________

Function?: _____________ Why or why not?:

5. Domain: ___________________ Range:

___________________

Function?: _____________ Why or why not?:

Algebra 2: Chapter 2 Review

Davis

Section 2: Evaluating Functions Evaluate the function for the given value of x. (2 pts) 6.

7.

f (x)

f (x)

3x 2

3x 2

4x 7 ; f

4x 7 ; f

3 8

2x 2

8.

f (x)

2

7, x

3

4 x 5,

3

x 1, x

2

2x 2 7, x

9.

f (x)

x

3

4 x 5,

3 x

x 1, x

2

Section 3: Graphing Functions Graph each function. Be sure to label any key points (intercepts, endpoints, and vertices). Show work when necessary. (3 pts) 10. f (x)

3 x 2 2

11. 2x 5y 9

12. 3y 9

13. 2x 9 0

2 ; f (2)

2 ; f ( 3)

Algebra 2: Chapter 2 Review 2x

14. f (x)

15. f (x)

4, x

3

x

3

4 x, 3

2x 3

4

Davis

4, 16. f (x)

0, 4, 2

17. 3x 2y 8

4

x

1 x 2 x 5

1

Algebra 2: Chapter 2 Review

Section 4: Writing Equations of Lines Write an equation of the line with the given characteristics. Write your answer in slope-intercept form and standard form when appropriate. If it is not possible to write in Standard Form, write n/a (not applicable). (3 pts) 18. through the point (-1, 3) and (-2, -3) Slope-Intercept Form (or other appropriate form) Standard Form

19. through the point (-2, 7) and parallel to the line, y = -4x + 3 Slope-Intercept Form (or other appropriate form) Standard Form

20. through the point (0, 7) and perpendicular to the line that passes through the points (7, -2) and (-4,-4) Slope-Intercept Form (or other appropriate form) Standard Form

21. through the point (13, 15) and parallel to y = -3. Slope-Intercept Form (or other appropriate form) Standard Form

22. through the point (-22, -25) and perpendicular to y = 7. Slope-Intercept Form (or other appropriate form) Standard Form

23. x and y vary directly and y = -3 when x = -13. Slope-Intercept Form (or other appropriate form) Standard Form

Davis

Algebra 2: Chapter 2 Review

Davis

Section 5: Linear Models and Best-Fit Lines Write an equation to model the situation or use your graphing calculator to write an equation of the best-fit line. Then answer the questions about each situation. Show your work in the space provided and write your answer in the appropriate blanks. (5 pts) 24. After the varsity basketball team began their current winning streak, attendance at games has steadily increased. After winning 3 games in a row, attendance was 570. After winning 8 games in a row, attendance was 1,030. If the team has currently won 11 games in a row, their next game is at home, and assuming that attendance has been increasing linearly, write a model to represent the situation and predict how many will be in attendance at the next home game.

Model Next Home Game’s Attendance

25. A local business has asked you to help them predict their sales for the next three years. They have given you the following data from the past 10 years of business. Use your graphing calculator to determine if there is a strong correlation in the data. If there is, approximate the equation of the best-fit line, state the correlation coefficient, and predict the businesses sales for each of the next three years. Round all decimals to the nearest hundredth. Year 1 2 3 4 5 6 7 8 9 10 11 Sales (ten 43.3 42.0 47.7 44.6 54.6 52.8 57.7 58.7 61.1 64.2 64.4 thousands)

Best-Fit Line Correlation Coefficient Sales (next three years)

$ $ $