Name: ______________________ Class: _________________ Date: _________ ID: A

1

Sample Final Questions - Chapter 2

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

Find the domain and range of the function represented by the graph.

1.

a. domain: 1, 2, 3, 4; range: –5, –4, –3, –2b. domain: –5, –4, –3, –2; range: 2, 3, 4, 5c. domain: 1, 2, 3, 4; range: 2, 3, 4, 5d. domain: 2, 3, 4, 5; range: –5, –4, –3, –2

Find the value of x so that the function has the given value.

2. q x( ) = 12

x − 15; q x( ) = −12

a. –18 c. 18b. 6 d. –6

Name: ______________________ ID: A

2

Graph the linear function.

3. g x( ) = −13

x + 2

a. c.

b. d.

Describe the slope of the line. Then find the slope.

4.

a. positive; 1 c. negative; –1b. zero; 0 d. positive; 4

Name: ______________________ ID: A

3

Write an equation of the line in slope-intercept form.

5.

a. y = 3 c. y = x − 3b. y = x + 3 d. y = −3

6.

a. y = 12

x + 3 c. y = 12

x – 3

b. y = 2x + 3 d. y = 2x – 3

Write an equation of the line that passes through the given points.

7. (–2, 4), (0, 7)

a. y = −4x – 4 c. y = −14

x + 72

b. y = –2 d. y = 32

x + 7

Name: ______________________ ID: A

4

Write an equation in point-slope form of the line that passes through the given point and has the given slope.

8. (–20, –5); m = 35

a. y = 35

x − 7 c. y + 5 = 35

x + 20( )

b. y = 35

x d. y − 5 = 35

x − 20( )

Write an equation in slope-intercept form of the line shown.

9.

a. y = 74

x + 4 c. y = 47

x + 4

b. y = −74

x – 4 d. y = −47

x – 4

Name: ______________________ ID: A

5

10. The path that you take to go from school to the library (shown in bold) is perpendicular to the path that takes you from home to the park. Write an equation that represents the path shown in bold.

a. y = x − 3 c. y = 4x − 1b. y = −x + 4 d. y = x + 4

Name: ______________________ ID: A

6

Multiple ResponseIdentify one or more choices that best complete the statement or answer the question.

1. Which of the following relations or graphs are functions?a. d.

b. e. Input,x −9 −3 2 9

Output,y 15 13 11 10

c. f. (−2,0),(0,2),(1,3),(2,4),(4,6)

2. Which equations represent linear functions? a. x − 9y = −7 d. y = x − 8| | − 2

b. y = 2x e. y − 3 = 4(x + 7)

c. y = −8 f. y = 5x2 + 2

Name: ______________________ ID: A

7

3. Which statements are true about the function 2x + y = 4?a. The y-intercept is 4. d. The x-intercept is 2.b. The graph of the function is: e. The graph of the function is:

c. The y-intercept is 2. f. The x-intercept is 4.

4. Which two pairs of points lie on perpendicular lines?a. −4,−5Ê

ËÁÁ ˆ

¯˜̃ , −3,−6ÊËÁÁ ˆ

¯˜̃

b. 4,−5ÊËÁÁ ˆ

¯˜̃ , 3,−6ÊËÁÁ ˆ

¯˜̃

c. 2,−3ÊËÁÁ ˆ

¯˜̃ , 0,−9ÊËÁÁ ˆ

¯˜̃

Short Answer

Does the graph represent a linear or nonlinear function? Explain.

1.

Evaluate the function when x = –3, 0, and 3.

2. h x( ) = x + 9

3. Graph x = 4.

Name: ______________________ ID: A

8

Use intercepts to graph the linear equation. Label the points corresponding to the intercepts.

4. 3x + 2y = 12

The points represented by the table lie on a line. How can you find the slope of the line from the table? What is the slope of the line?

5. x 2 4 6 8y 0 2 4 6

Find the slope and y-intercept of the graph of the linear equation.

6. y + 2 = 12

x

7. 2x − 2y = −12

Graph the linear equation. Identify the x-intercept.

8. y = −x − 3

9. −x + y = 3

10. An alligator is 8 inches long at birth and grows 10 inches per year. Write an equation that represents the length y (in feet) of an alligator that is x years old. How long will the alligator be after 7 years?

11. The high school Pep Club is ordering T-shirts for student members. The table below shows the cost y (in dollars) of ordering different numbers x of T-shirts.

Number of T-shirts 22 28 34 40 46

Cost (in dollars) 243 303 363 423 483

a. Can the situation be modeled by a linear equation? How do you know?

b. Write a linear model for this data if possible.

c. According to the model, how much will it cost to purchase 58 T-shirts?

Name: ______________________ ID: A

9

Determine which lines, if any, are parallel? Explain.

12.

13. Line a: 2y − 4x = 6

Line b: 2y = 5x + 8

Line c: 2y − 6x = 4

Problem

1. Write an equation of a line in slope-intercept form that passes through the point (- 4, - 2) and is parallel to the line y = 4x - 8.

2. Write an equation of a line in slope intercept for that is perpendicular to the line y = - 2x + 9 and goes through the point (6, 1)

Other

1. The function n = −2b + 12 represents the number of eggs n left in the carton after making b breakfast sandwiches.

a. Identify the independent and dependent variables.

b. The domain is 1, 2, 3, and 4. What is the range?

2. Let s(t) be the speed (in meters per second) of an object after t seconds of motion. Explain the meaning of each statement.

a. s(0) = 3

b. s(6) = k

c. s(10) < s(13)

Name: ______________________ ID: A

10

3. The cost y (in dollars) of getting into a fair and riding x rides is C(x) = 1.25x + 6. You only have a total of $21 to spend at the fair.

a. Graph the function and identify its domain and range.

b. Interpret the slope and the intercepts of the graph.

4. The number m of miles a long-distance cyclist travels during today’s ride can be modeled by the function m(t) = 12t + 40, where t represents the number of hours since a noon rest stop.

a. Graph the function and interpret the slope and m-intercept.

b. The cyclist can only ride until 8:00 P.M. Identify the domain and range of the function.

c. The cyclist will meet up with friends 100 miles from the morning’s starting location. Will the cyclist get there today? Explain.

5. A store receives a shipment of 380 skateboard wheels. After 3 days, 317 of the skateboard wheels are left. After 7 days, 233 skateboard wheels are left.

a. Write an equation that represents the number y of skateboard wheels remaining after x days.

b. Use the linear equation to predict how many skateboard wheels will be left after 10 days.

c. After how many days should the store plan to receive a new shipment of skateboard wheels so they do not run out?

d. What does the slope of the equation represent? What does the y-intercept represent?

ID: A

1

Sample Final Questions - Chapter 2Answer Section

MULTIPLE CHOICE

1. B 2. B 3. D 4. B 5. A 6. C 7. D 8. C 9. B 10. D

MULTIPLE RESPONSE

1. C, D, E, F 2. A, C, E 3. A, B, D 4. A, B

SHORT ANSWER

1. linear; The graph is a line. 2. h −3( ) = 6, h 0( ) = 9, h 3( ) = 12

3.

ID: A

2

4.

5. Choose any two points from the table and use the slope formula; 1

6. slope: 12

, y-intercept: –2

7. slope: 1, y-intercept: 6

8.

x-intercept: –3

ID: A

3

9.

x-intercept: –3

10. y = 56

x + 23

; 612

ft long

11. a. Yes. The rate of change for consecutive data pairs is constant; therefore, the relationship is linear.b. y = 10x + 23c. $603.00

12. The second and third lines are parallel. They both have a slope of −2. 13. None of the lines are parallel. None of them have the same slope.

PROBLEM

1. y = 4x + 14 2. y = 1/2x - 2

OTHER

1. a. n is the dependent variable and b is the independent variable.b. 10, 8, 6, 4

2. a. The starting speed at t = 0 is 3 meters per second.b. The speed at 6 seconds is k meters per second.c. The speed at 10 seconds is less than the speed at 13 seconds. The object is speeding up.

ID: A

4

3. a.

domain: 0 ≤ x ≤ 12; range: 6 ≤ y ≤ 21

b. The slope of 1.25 means that it costs $1.25 for every ride. The y-intercept of 6 means that the cost to get into the fair is $6.00. The graph does not have an x-intercept.

4. a.

The slope is the speed of the cyclist, 12 miles per hour. The m-intercept is the number of miles traveled before noon, 40 miles.

b. domain: 0 ≤ t ≤ 8, range: 40≤ m ≤ 136c. yes; The cyclist will travel 100 miles before 8:00 P.M.

5. a. y = −21x + 380b. 170 skateboard wheelsc. 18 daysd. The slope represents the decrease in inventory due to the number of skateboard wheels sold each day. The

y-intercept represents the number of skateboard wheels received in the shipment.