ALG. 2 CH 2 TEST REVIEW

Multiple Choice range: range: Identify the choice that best completes the statement or answers the question.

____ 1. Make a mapping diagram for the relation. ____ 3. Find the domain and range of the relation and {(–3, 1), (0, 6), (3, 2), (5, –1)} determine whether it is a function.

y a. c. 8 –3 –1 –3 0 0 1 1 6 4 3 2 3 5 5 6 2 –1 –8 –4 O 4 8 x –4 b d . –3 –1 . –3 1 –8 0 2 0 6 3 6 3 2 –3 5 1 5 –1 a. domain: all real numbers; range: all real numbers; Yes, it is a function. ____ 2. Graph the relation. Find the domain and range. b. domain: positive integers; range: positive integers; No, it is not a function. c. domain: x  0; range: y  3; No, it is not a function.

y y d. domain: x > 3; range: y > 0; Yes, it is a a. c. function. 4 4

O –4 4 x –4 O 4 x

–4 –4

domain: domain:

range: Is the relation a function? range:

b y d y . 4 . 4 4 10 ____4. 7 8 10 14 –4 O 4 x –4 O 4 x 12 11

–4 –4

domain: domain: a. yes b. no a. yes; k = 1.6; y = c. yes; k = 6; ____ 5. Use the vertical-line test to determine which 1.6x graph represents a function. b. yes; k = 3; d. no

a. y c. y Determine whether y varies directly with x. If 8 8 so, find the constant of variation k. 4 4 ____ 9. –3y = –5x –8 –4 O 4 8 x –8 –4 O 4 8 x –4 –4 a. yes; –5 b. 3 c. 5 d. no –8 –8 yes; yes; 5 3 b y d y . 8 . 8 Find the value of y for a given value of x, if y

4 4 varies directly with x.

–8 –4 O 4 8 x –8 –4 4 8 x ____ 10. If y = 44 when x = –264, what is y when x = – –4 –4 486? –8 –8 a. –2916 b. –81 c. 2916 d. 81 ____ 11. A leaky valve on the water meter overcharges For each function, what is the output of the given input? the residents for one gallon of water every months. The overcharged amount w varies ____ 6. For , . directly with time t. Find the equation that models this direct variation. How many months a. 9 b. –17 c. –3 d. 17 it will take for the residents to be overcharged ____ 7. Specialty t-shirts are being sold online for $15 for 9 gallons of water? each, plus a one-time handling fee of $2.25. The total cost is a function of the number of t-shirts a. 7 c. ; 2 ; 30 bought. What function rule models the cost of 10 the t-shirts ( )? Evaluate the function for 3 t- months months shirts. b. d. 7 ; 30 ; 2 10 a. ; $21.75 c. ; $47.25 months months b. ; $47.25 d. ; $21.75 What is the graph of each direct variation Determine whether y varies directly with x. If equation? so, find the constant of variation k and write the equation. ____ 12.

____ 8. a. c. x y y y 8 8

6 9.6 4 4 9 14.4 –8 –4 4 8 x –8 –4 4 8 x 12 19.2 –4 –4 –8 –8 15 24 b. d. y y y 8 8

4 4 8

–8 –4 4 8 x –8 –4 4 8 x –4 –4 4 –8 –8

____ 13. –8 –4 4 8 x –4 a. c. y y –8 8 8

4 4 ____ 16. –8 –4 4 8 x –8 –4 4 8 x a. c. –4 –4 b. d.

–8 –8

b d . y . y 8 8

4 4 Write the equation in slope-intercept form. What are the slope and y-intercept? –8 –4 4 8 x –8 –4 4 8 x –4 –4 ____ 17. –8 –8 a. 5 c. 5 3 ; 3 ; 2 2 slope: 3; y- 5 slope: ; y- What is the slope of the line that passes 5 2 through the given points? intercept: 2 intercept: 3 b. 5 d. 5 ____ 14. (–12, –4) and (11, –10) 3 3 ; 2 2 a. 23 c. 6   slope: 3; y-intercept: slope: 3; y- 6 23 5 5 b. 23 d. 6 intercept: 2 2 6 23

What is an equation of the line in slope What is the graph of the equation? intercept form? ____ 18. 1 ____ 15. m = and the y-intercept is (0, –5) a. c. 2 y y

a. 1 c. 1 8 8 2 2 4 4 b. 1 d. 1 + 2 2 –8 –4 4 8 x –8 –4 4 8 x –4 –4

–8 –8 2 ____ 21. point: ; slope: 5

b d a. 2 c. 2 y y . . 5 5 8 8 b. 2 d. 2 4 4 5 5

–8 –4 4 8 x –8 –4 4 8 x –4 –4 What is the equation of the given line in

–8 –8 standard form? Use integer coefficients.

____ 22. ____ 19. a. c. a. c. y y b. d.

8 8

4 4

–8 –4 4 8 x –8 –4 4 8 x –4 –4 –8 –8 What are the intercepts of the equation? Graph the equation.

b. d. y y ____ 23.

8 8 a. x-intercept: (–4, 0) c. x-intercept: (4, 0) 4 4 y-intercept: (0, 4) y-intercept: (0, –4) y y –8 –4 4 8 x –8 –4 4 8 x –4 –4 8 8

–8 –8 4 4

–8 –4 4 8 x –8 –4 4 8 x –4 –4

–8 –8

Write an equation of the line, in point-slope b x-intercept: (–4, 0) d x-intercept: (4, 0) form, that passes through the two given . y-intercept: (0, 4) . y-intercept: (0, –4) points. y y 8 8

____ 20. points: , 4 4

–8 –4 4 8 x –8 –4 4 8 x a. 1 c. –2 –4  –4 2 –8 –8 b. –2 d. 1  2 ____ 24. The equation and the table below What is an equation of the line, in point-slope each represent linear functions. Which has the form, that passes through the given point and greater slope, and what is its value? has the given slope? x -2 -1 0 1 2 y 2 4 6 8 10 Make a scatter plot and describe the correlation.

____ 27. The table lists the results from a survey (of a. The table c. The table questionable accuracy) of adults and how much Slope = 0.5 Slope = 2 they spend on a night out. The table displays the values rounded to the nearest whole number. b. The equation d. The equation Make a scatter plot. How would you describe Slope = –1 Slope = 1 the correlation between a person's age and how much he or she spends on a night out? ____ 25. The office manager of a small office ordered 180 packs of printer paper. Based on average Age Average cost daily use, she knows that the paper will last (years) of a night out ($) about 40 days. What graph represents this 21 54 situation? How many packs of printer paper 16 50 should the manager expect to have after 35 22 47 days? 24 42 28 38 a c 30 35 paper paper . . 33 40 150 150 36 35

100 100

50 50 a c cost cost 20 40 60 days . 80 . 80 20 40 60 days 2 1 2.5 packs 57.5 packs 60 b d 60 . paper . paper 40 40 150 150

100 100 20 40 age 20 40 age

50 50 As age increases, the As age increases, the average cost average cost 20 40 60 days 20 40 60 days 1 increases; there is a decreases; there is a positive correlation. 22.5 packs 57.5 packs positive correlation. b d cost cost What is the equation of the line in slope- . 80 . 80 intercept form? 60 60 1 ____ 26. the line perpendicular to through (2, 3 40 40 1)

a. 1 c. 3 20 40 age 20 40 age 3 As age increases, the As age increases, the b. 3 d. 1 average cost average cost 3 decreases; there is a increases; there is a negative correlation. negative correlation. ____ 28. A 3-mi cab ride costs $7.90. A 9-mi cab ride Year 198 198 199 1995 2000 2005 costs $18.70. Find a linear equation that models 0 5 0 a relationship between cost c and distance d. Member 5,1 6,5 8,1 10,5 12,0 12,6 a. c = 1.80d + 2.50 c. c = 2.63d + 10.80 ship 00 00 00 00 00 00 b. c = 2.08d + 2.50 d. d = 1.80c + 10.80 ____ 29. A candle is 18 in. tall after burning for 3 hours. a. ; c. ; After 5 hours, it is 16.5 in. tall. Write a linear 27,438 17,938 equation to model the relationship between b. ; d. ; height h of the candle and time t. Predict how 27,438 17,938 tall the candle will be after burning 8 hours. ____ 32. How are the functions and related? How are their graphs related? a c . . b d a. Each output for is 5 less than the . . corresponding output for . The graph of is the graph of Graph the set of data. Decide whether a translated down 5 units. linear model is reasonable. If so, draw a trend b. Each output for is 5 more than the line and write its equation. corresponding output for . The graph of is the graph of translated up 5 units. ____ 30. {(1, 3), (–2, 1), (3, ), (–4, –3), (0, 5)} c. Each output for is 5 more than the a yes; c a linear model is corresponding output for . . y . not reasonable The graph of is the graph of 12 y translated down 5 units. 12 8 d. Each output for is 5 less than the

8 4 corresponding output for .

4 The graph of is the graph of –8 –4 O 4 8 12 x translated up 5 units. –4 –4 O 4 8 12 x –4 ____ 33. The graph shows the projected altitude (in thousands of feet) of an airplane scheduled b d yes; to depart an airport at noon. If the plane leaves yes; . . y two hour(s) late, what function represents this y 8 transformation?

12 4 altitude 8 –8 –4 O 4 8 x 20 4 –4

–8 –4 O 4 8 12 x 10 –4

____ 31. A nationwide club begins a chapter near you. –10 –8 –6 –4 –2 2 4 6 pm hours You research the membership of the club over the past few decades. The table shows your –10 data. What is the equation for a line of best fit? How many members would you expect there to be in the year 2019? –20 10 5 a c altitude altitude . 20 . 20

10 10

–10 –8 –6 –4 –2 2 4 6 pm hours –10 –8 –6 –4 –2 2 4 6 pm hours

–10 –10

–20 –20 The function The function a. x g ( x ) c. x g ( x )

represents this represents this transformation. transformation. b d altitude altitude . 20 . 20

10 10

–10 –8 –6 –4 –2 2 4 6 pm hours –10 –8 –6 –4 –2 2 4 6 pm hours b. x g ( x ) d. x g ( x )

–10 –10

–20 –20 The function The function

represents this represents this transformation. transformation.

Let g(x) be the reflection of f(x) in the x-axis. Find the function rule for g(x). What is the function rule for g(x)? ____ 36. The function . The graph of is ____ 34. Let be the reflection of in the vertically stretched by a factor of 7 and x-axis. What is a function rule for ? reflected in the x-axis. What is the function rule for ? a. c. b. d. a. 6 c. 6  x x 7 7 The function f(x) is represented by the given b. 42x d. –42x table. What are the corresponding values of the given g(x)? What transformations change the graph of f(x) to the graph of g(x)? ____ 35. The function is represented by the table below. What are the corresponding ____ 37. values of for the transformation ? a. The graph of is the graph of x stretched vertically by a factor of 3 and translated up 4 units. –7 8 b. The graph of is the graph of –3 3 1 0 –1 stretched vertically by a factor of and 3 2 7 translated up 4 units. units to the left and units to the right and c. The graph of is the graph of 7 units down 7 units down stretched vertically by a factor of 3 and b. translated 2 d. translated 7 translated down 4 units. units to the right and units to the left and d. The graph of is the graph of 7 units up 2 units down 1 stretched vertically by a factor of and 3 What is the graph of the absolute value translated down 4 units. function?

1 What is the graph of the absolute value ____ 41.  equation? 3

____ 38. a. y c. y 12 12

a. y c. y 6 6 8 8 O –12 –6 6 12 x –12 –6 O 6 12 x 4 4 –6 –6

–8 –4 O 4 8 x O –12 –8 –4 4 8 x –12 –4 –4

–8 y y –8 b d . 12 . 12 b y d y 6 6 . 8 . 8 –12 –6 O 6 12 x –12 –6 O 6 12 x 4 4 –6 –6

O O –8 –4 4 8 x –8 –4 4 8 x –12 –12 –4 –4

–8 –8 ____ 42. a. y c. y 12 12 ____ 39. a. y c. y 6 6 12 12

–12 –6 O 6 12 x –12 –6 O 6 12 x 6 6 –6 –6

O –12 –6 O 6 12 x –12 –6 6 12 x –12 –12 –6 –6 y y –12 b d –12 . 12 . 12 b y d y 6 6 . 12 . 12 –12 –6 O 6 12 x –12 –6 O 6 12 x 6 6 –6 –6

O O –12 –6 6 12 x –12 –6 6 12 x –12 –12 –6 –6

–12 –12

____ 40. Which of the following describes the translation of to ? a. translated 2 c. translated 7 Compare each function with the parent What is the equation of the absolute value function. Without graphing, what are the function? vertex, axis of symmetry, and transformations of the parent function? ____ 45. y 12

8

____ 43. 4 a. 5 5 ( , 4) x =  ; –10 –8 –6 –4 –2 2 x 4 4 –4 –8

5 –12 translated to the left units and up 4 units. 4 –16 b. 5 5 ( , –4); x = ; 4 4 a. y = c. y = 5 translated to the left units and down 4 b. y = d. y = 4 units. What is the graph of each inequality? c. 5 5 ( , 4); x = ; 4 4 ____ 46. –4x + 4y  4 5 y y translated to the left units, up 4 units, and a. c. 4 12 12 8 reflected in the y-axis. 8 4 4

O –12 –8 –4 4 8 12 x –12 –8 –4 O 4 8 12 x d. 5 5 –4 ( , –4); x =  ; –4 4 4 –8 –8 –12 5 –12 translated to the right units and up 4 units. 4 b y d y 12 ____ 44. . 12 . 8 8 a. 5 5 4 ( , 2); x =  ; 4 4 4 –12 –8 –4 O 4 8 12 x O –12 –8 –4 4 8 12 x –4 5 –4 translated to the left units and up 2 units –8 –8 4 –12 b. 5 5 –12 ( , 2); x = ; 4 4 ____ 5 translated to the right units and up 2 units, 4 and reflected in the y-axis. c. 5 5 ( , –2); x =  ; ____ 47. 4 4 a y c y 5 12 12 translated to the left units, up 2 units, and . . 4 8 8 reflected in the x-axis. 4 4 d. 5 5 –12 –8 –4 O 4 8 12 x –12 –8 –4 O 4 8 12 x ( , –2); x = ; –4 –4 4 4 –8 –8 5 –12 translated to the right units and down 2 –12 4 units b y d y b y d y . 12 . 12 . 12 . 12 8 8 6 6 4 4

O O –12 –8 –4 O 4 8 12 x –12 –8 –4 O 4 8 12 x –12 –6 6 12 x –12 –6 6 12 x –4 –4 –6 –6 –8 –8 –12 –12 –12 –12

____ 48. A doctor’s office schedules 15-minute appointments and half-hour appointments for weekdays. The doctor limits these appointments to, at most, 30 hours per week. Write an inequality to represent the number of 15-minute appointments x and the number of half-hour appointments y the doctor may have in a week. a. c. b. d.

What is the graph of each absolute value inequality?

____ 49. y  |x – 1| + 3 a. y c. y 12 12

6 6

O –12 –6 6 12 x –12 –6 O 6 12 x

–6 –6

–12 –12

b y d y . 12 . 12 6 6

–12 –6 O 6 12 x –12 –6 O 6 12 x

–6 –6

–12 –12

____ 50. |x + 5|  y – 2 a. y c. y 12 12

6 6

–12 –6 O 6 12 x –12 –6 O 6 12 x

–6 –6

–12 –12 CH 2 TEST REVIEW 42. ANS: D Answer Section 43. ANS: C 44. ANS: C 45. ANS: D MULTIPLE CHOICE 46. ANS: B 47. ANS: B 1. ANS: A 48. ANS: B 2. ANS: A 49. ANS: C 3. ANS: D 50. ANS: A 4. ANS: A 5. ANS: B 6. ANS: C 7. ANS: C 8. ANS: A 9. ANS: C 10. ANS: D 11. ANS: B 12. ANS: D 13. ANS: A 14. ANS: C 15. ANS: A 16. ANS: C 17. ANS: A 18. ANS: A 19. ANS: A 20. ANS: A 21. ANS: A 22. ANS: B 23. ANS: C 24. ANS: C 25. ANS: B 26. ANS: B 27. ANS: B 28. ANS: A 29. ANS: A 30. ANS: C 31. ANS: C 32. ANS: B 33. ANS: A 34. ANS: A 35. ANS: D 36. ANS: B 37. ANS: C 38. ANS: C 39. ANS: A 40. ANS: D 41. ANS: D