Working With Different Types of Graphs

Linear graphs

Which inequality best describes the graph shown to the right? A y ≥ – 2x B y ≥ –x – 2 C y ≥ –2x – 2 D y ≥ x – 2 Obj 1 - TAKS th [A.B1(D)] Problem #6

Which coordinate points represent the x- and y-intercepts of the graph shown to the right? A (0, –4) and (6, 0) B (–4, 0) and (0, 6) C (6, 0) and (–4, 0) D (0, 6) and (0, –4) Obj 3 - TAKS th [A.C2(E)] Problem #6

What is the slope of the linear function shown in the graph? A B C D Obj 3 - TAKS th [A.C2(A)] Problem #3

Which graph best represents the inequality x + 2y ≤ –14? Obj 1 - TAKS th [A.B1(D)] Problem #3

What is the rate of change of the graph to the right? A 3.5 B 1.67 C 0.6 D –1.67 Obj 3 - TAKS th [A.C2(A)] Problem #8

Which graph best represents all the pairs of numbers (x, y) such that x + y < –6? Obj 1 - TAKS th [A.B1(D)] Problem #29

Which inequality best describes the graph shown below? A. B. C. D. Obj 1 - TAKS th [A.B1(D)] Problem #31

What are the x- and y-intercepts of the function graphed to the right? A (4, 0) and (5, 0) B (4, 0) and (0, 5) C (0, 4) and (5, 0) D (0, 4) and (0, 5) Obj 3 - TAKS th [A.C2(E)] Problem #5

What will happen to the slope of line p if the line is shifted so the the y-intercept increases and the x-intercept remains the same? Obj 3 - TAKS th [A.C2(C)] A The slope will change from positive to negative. B The slope will change from negative to positive. C The slope will increase. D The slope will decrease. Problem #7

Which graph best represents the function y = –1.75x + 5 Obj 3 - TAKS th [A.C1(C)] Problem #10

The graph of a line is shown to the right. If the slope of this line is multiplied by –1 and the y-intercept decreases by 2 units, which linear equation represents these changes? A B C D Obj 3 - TAKS th [A.C2(C)] Problem #11

What are the slope and y-intercept of the equation of the line graphed below? A B C D Obj 3 - TAKS th [A.C2(A)] Problem #14

Which linear function includes the points (–3, 1) and (–2, 4)? A. B. C. D. Obj 3 - TAKS th [A.C2(D)] Problem #15

The graph of a line that contains the points (–1, –5) and (4, 5) is shown below. Obj 3 - TAKS th [A.C2(C)] Problem #19

Which graph best represents this line if the slope is doubled and the y- intercept remains constant? Obj 3 - TAKS th [A.C2(C)] Problem #19

Which best describes the effect on the graph of f(x) = 4x + 8 if the y-intercept is changed to –3? Obj 3 - TAKS th [A.C2(C)] A. The slope decreases. B. The new line passes through the origin. C. The x-intercept increases. D. The y-intercept increases. Problem #21

Which linear function best describes the graph shown to the right? A. B. C. D. Obj 3 - TAKS th [A.C1(C)] Problem #23

What is m, the slope of the line that contains the points (2, 0), (0, 3), and (4, –3)? A. B. C. D. Obj 3 - TAKS th [A.C2(A)] Problem #24

What is the y-intercept of the function graphed to the right? A. –24 B. –21 C. –18 D. –9 Obj 3 - TAKS th [A.C2(E)] Problem #25

Which line appears to have a slope of zero? F. Line n G. Line k H. Line w J. Line p Obj 3 - TAKS th [A.C2(A)] Problem #38

What are the slope and y-intercept of a line that contains the point (5, –1) and has the same y-intercept as x – 3y = 6? A. B. C. D. Obj 3 - TAKS th [A.C2(B)] Problem #29

The graph of a linear function is shown below. If the line is translated 2 units down, which equation will best describe the new line? F. y = 3x + 1 G. y = x + 1 H. y = 3x + 5 J. y = x + 5 Obj 3 - TAKS th [A.C2(C)] Problem #41

The graphs of the linear equations y = 2x – 3 and y = 3x – 7 are shown to the right. If 2x – 3 = 3x – 7, what is the value of x? A 4 B 5 C 9 D 10 Obj 4 - TAKS th [A.C3(B)] Problem #4

Which linear equation represents the line passing through points R and S? F. y = 1.5x − 4.5 G. y = 1.5x H. y = 0.5x − 4.5 J. y = 0.5x Obj 3 - TAKS th [A.C2(D)] Problem #35

Which graph best represents the line that has a slope of − and contains the point (4, −3)? Obj 3 - TAKS th [A.C2(D)] Problem #40

Which graph below best represents the linear parent function? Obj 2 - TAKS th [A.B2(A)] Problem #33

Which graph best represents a solution to this system of equations? 2x – 3y = 0 x + 2y = –7 Obj 4 - TAKS th [A.C4(B)] Problem #24

Which graph best represents a line that is parallel to the graph of the equation y = – x − 2? Obj 7 - TAKS th [G.D2(B)] Problem #53

What is the slope of the line that contains the coordinate points (8, −3) and (−2, 7)? A. −1 C. B. D. Obj 3 - TAKS th [A.C2(A)] Problem #33

Mr. Maxwell asked his students to identify the domain represented by the function graphed below. Which of the following student responses is correct? F. −5 x < 6 G. −6 x 2 H. −5 x < −2 J. Not here Obj 2 - TAKS th [A.B2(B)] Problem #42

A shaded parallelogram is graphed on the coordinate grid to the right. Which of the following functions describes a line that would include an edge of the shaded parallelogram? A y = –2x + 5 B y = –2x – 2 C y = –2x + 9 D y = –2x – 1 Obj 4 - TAKS th [A.C3(A)] Problem #5

If the system of linear equations 2x + y = 1 and y = − ½ x + 1 are graphed on the same coordinate grid, which of the following is the solution to this system of linear equations? A. (2, 0) B. (0, 2) C. (0.5, 0) D. Not here Obj 4 - TAKS th [A.C4(B)] Problem #38

The graph of the equation is given to the right. Graph y = x + 1 on the grid. What is the solution to this system of equations? A (0, 1) B (5, 6) C (6, 7) D No solution Obj 4 - TAKS th [A.C4(B)] Problem #10

Word Problems-Graphs

The line segment on the graph shows the altitude of a landing airplane from the time its wheels are lowered to the time it touches the ground. Which of the following best describes the slope of the line segment? Obj 3 - TAKS th [A.C2(B)] A The plane descends about 1 foot per 8 seconds. B The plane descends about 8 feet per second. C The plane descends about 1 foot per 2 seconds. D The plane descends about 2 feet per second. Problem #4

Which statement is true for the graph to the right? Obj 2 - TAKS th [A.B2(C)] A Ms. Goodlett will earn $500 if she sells $5000 worth of merchandise. B Mr. Murphy will not earn any money if he does not sell any merchandise. C Mr. Laster will earn $1000 if he sells $1000 worth of merchandise. D Ms. Cho will earn $700 if she sells $5000 worth of merchandise. Problem #5

A small business purchased a van to handle its delivery orders. The graph below shows the value of this van over a period of time. Which of the following best describes this situation? A. The van was purchased for $1,600. B. The van decreases in value by $1,600 per year. C. The van increases in value by $1,600 per year. D. The van has no value after 5 years. Obj 3 - TAKS th [A.C2(B)] Problem #30

The graph of a linear function is shown on the coordinate grid below. If the y-intercept is changed to (0, 5) and the slope becomes −4, which statement best describes the relationship between the two lines when they are graphed on the same coordinate grid? F. The y-intercepts are 1 unit apart, and the lines are parallel. G. The y-intercepts are 1 unit apart, and the lines intersect at (1, 1). H. The y-intercepts are 1 unit apart, and the lines are perpendicular. J. The y-intercepts are 1 unit apart, and the lines intersect at (1, 0). Obj 3 - TAKS th [A.C2(C)] Problem #31

The graph shows the distance a certain motorbike can travel at a constant speed with respect to time. Which of the following best describes the meaning of the slope of the line representing this situation? F. The motorbike travels at a speed of about 8 miles per hour. G. The motorbike travels at a speed of about 2.5 miles per hour. H. The motorbike travels at a speed of about 5 miles per hour. J. The motorbike travels at a speed of about 10 miles per hour. Obj 3 - TAKS th [A.C2(B)] Problem #36

Obj 2 - TAKS th [A.B2(C)] The graph below shows the decrease in the value of a personal computer over a period of 60 months. Problem #15

Obj 2 - TAKS th [A.B2(C)] Which is a reasonable conclusion about the value of this personal computer during the time shown on the graph? A Its value at 18 months was twice its value at 36 months. B Its value at 36 months was half its value at 54 months. C It depreciated $200 every 12 months. D It depreciated $400 every 18 months. Problem #15

At the Dallas–Fort Worth International Airport, a DC-10, at 4500 feet, is descending toward the east runway at a rate of 150 feet per minute, and a 727, at 600 feet, is climbing at a rate of 75 feet per minute. Which graph shows when the two planes will be at the same altitude? Obj 2 - TAKS th [A.B2(C)] Problem #28

Look at the graph below. Which is the best interpretation of this graph? A. Jorge earns $20 for each hour worked. B. For every 10 pieces of candy Stacey buys, she pays $1. C. For every 10 students at a dance, 2 teachers are needed as chaperones. D. A runner runs at a constant rate of 2 miles every 30 minutes. Obj 2 - TAKS th [A.B2(C)] Problem #35

The graph below shows the amount of force needed to stretch a certain spring to various distances. Which of the following best represents the difference between the amount of force in pounds needed to stretch the spring to 10 inches and the amount needed to stretch it to 4 inches? F. 6 G. 14 H. 30 J. 70 Obj 2 - TAKS th [A.B4(A)] Problem #43

Valerie purchased x tubes of lipstick at $4 each and y bottles of nail polish at $2 each. She spent less than $12, not including tax. Use the grid to the right to graph the inequality 4x + 2y < 12. Which point represents a reasonable number of lipsticks and bottles of nail polish that Valerie purchased? A. (1, 5) B. (2, 3) C. (1, 3) D. (2, 2) Obj 4 - TAKS th [A.C3(C)] Problem #29

The graph of a system of linear equations is shown below. Which of the following is the solution to this system of linear equations? F. (0, 4) G. (8, 1) H. (0, −3) J. (10, 2) Obj 4 - TAKS th [A.C4(B)] Problem #43

Karen jogs at a steady pace up a hill in her neighborhood. She then runs down the hill, and her speed increases. Which graph best describes this situation? Obj 1 - TAKS th [A.B1(E)] Problem #2

Which is the best representation of the function y = x? A.C. B.D. Obj 2 - TAKS th [A.B2(A)] Problem #16

The graph below shows the relationship between the distance in miles a delivery truck traveled and the number of hours each delivery took. Which best describes the relationship shown on the graph? A. Negative trend B. Positive trend C. Constant trend D. No trend Obj 2 - TAKS th [A.B2(D)] Problem #34

In the distance formula d = rt, r represents the rate of change, or slope. Which ray on the graph best represents a slope of 55 mph? A. W B. X C. Y D. Z Obj 3 - TAKS th [A.C2(A)] Problem #18

The graph to the right best represents which of the following relationships between temperature and time? Obj 1 - TAKS th [A.B1(E)] A Oven temperature while a cake is baking B Temperature of water that is heated on a stove, removed, and then allowed to cool C Temperature of a container of hot tea after placing several cubes of ice in it D Room temperature of a gym after the air conditioner is turned on Problem #10

Which graph best represents the relationship between the height of a burning candle and the amount of time that passes as the candle burns? Obj 1 - TAKS th [A.B1(E)] Problem #13

Identify the graphs that best represents the relationship between the number of gallons of gasoline Mr. Johnson purchased at $1.49 a gallon and the total cost of his gasoline. Obj 2 - TAKS th [A.B2(C)] Problem #20

Gina did a research project on how age affects sleep patterns. She concluded that as people age, they sleep fewer hours until a point in adulthood when the number of hours remains constant. Gina also found that after the age of 70 the amount of time spent sleeping increases slightly. Which graph best shows the results of Gina’s research? Obj 1 - TAKS th [A.B1(E)] Problem #30

Problem #34 Obj 5 - TAKS th [A.D1(D)] An object was dropped from a height of 250 meters and fell to the ground. The graph below shows the change in h, the object’s height in meters, with respect to t, the time in seconds. According to the graph, which time interval best represents when the object was at 140 meters above the ground? F. Between 3 seconds and 3.25 seconds G. Between 3.75 seconds and 4 seconds H. Between 3.5 seconds and 3.75 seconds J. Between 3.25 seconds and 3.5 seconds

The graph below represents Lynne’s car trip from her house to the mall and then back to her house. If each section of the graph represents part of Lynne’s trip, which part of the trip took the least amount of time? A. r B. p C. q D. s Obj 1 - TAKS th [A.B1(E)] Problem #34

The graph below represents Cheyenne’s bicycle trip from her house to a friend’s house. On which segment of the graph does it appear that Cheyenne was riding her bicycle at the slowest pace? A. r B. s C. t D. u Obj 1 - TAKS th [A.B1(E)] Problem #40

Obj 2 - TAKS th [A.B2(D)] The coaches of a group of debate teams answered a survey about hours of debate team practice and number of team wins. The graph shows the results of this survey. Based on these results, if a team practices 4 hours per week next season, which is the best estimate of the number of debates the team can expect to win? A 1 B 12 C 16 D 20 Problem #8

Quadratic graphs

Obj 2 - TAKS th [A.B2(B)] What is the domain of the function shown on the graph? A –3 ≤ x ≤ 3 B –3 < x < 3 C –5 < x ≤ 4 D –5 ≤ x < 4 Problem #12

Obj 2 - TAKS th [A.B2(A)] Which equation is the parent function of the graph represented to the right? A B C D Problem #13

Jake studied the parabola shown to the right. Which is an accurate conclusion that Jake could make about this parabola? A. The vertex is at (–2, 0). B. The minimum value is at (0, –4). C. The maximum value is at (2, 0). D. The axis of symmetry is the x-axis. Obj 1 - TAKS th [A.B1(E)] Problem #23

The graph shows the path of a golf ball. What is the range of this function? A. 0 < y < 100 B. 0 ≤ y ≤ 100 C. 0 ≤ x ≤ 5 D. 0 < x < 5 Obj 2 - TAKS th [A.B2(B)] Problem #22

Which graph shows a function y = x 2 + c when c < –1? Obj 5 - TAKS th [A.D1(C)] Proble m #2

What are the roots of the function graphed to the right? A (–1, –9) and (0, –8) B (0, –4) and (2, 0) C (–4, 0) and (2, 0) D (0, 2) and (0, –4) Obj 5 - TAKS th [A.D2(B)] Proble m #7

The graph to the right shows h, the height in meters of a model rocket, versus t, the time in seconds after the rocket is launched. From the graph, what conclusion can be made about the flight of the rocket? Obj 5 - TAKS th [A.D1(D)] A The rocket reached its maximum height after 2.5 seconds. B At 0 seconds the rocket was 2 meters off the ground. C The height of the rocket was 0 meters when it was launched. D The rocket was in flight for 5 seconds. Proble m #9

The graph to the right shows the height of a baseball from the time it is thrown from the top of a building to the time it hits the ground. How much time elapses while the baseball is 80 meters or more above the ground? A 1 sec B 9 sec C 7 sec D 6 sec Obj 5 - TAKS th [A.D1(D)] Problem #10

When graphed, which function would appear to be shifted 2 units up from the graph of f(x) = x 2 + 1? A. g(x) = x 2 – 1 B. g(x) = x C. g(x) = x 2 – 2 D. g(x) = x Obj 5 - TAKS th [A.D1(C)] Problem #18

The sales record for a recent hit CD at Tony’s Music Store is shown on the graph to the right. Which statement best describes the sales of this CD? Obj 5 - TAKS th [A.D1(D)] A. Sales rapidly increased, reached a peak, and then gradually decreased. B. Sales gradually increased, reached a peak, and then leveled off. C. Sales rapidly increased, reached a peak, and then rapidly decreased. D. Sales remained constant throughout the time period. Problem #19

The graph of the function y = x 2 is given to the right. How will the graph be affected if the coefficient of x 2 is decreased to ¼? Obj 5 - TAKS th [A.,D1(B)] A. The parabola will be wider. B. The parabola will be narrower. C. The parabola will be translated up. D. The parabola will be translated down. Problem #20

The graph of a function is shown below. Problem #29 Obj 5 - TAKS th [A.D1(C)] If the graph is translated 7 units down, which of the following best represents the resulting graph?

Problem #29 Obj 5 - TAKS th [A.D1(C)]

Problem #31 Obj 5 - TAKS th [A.D1(C)] F. y = x G. y = x H. y = x 2 − 2 J. y = x 2 − 8 The graph of the function y = x 2 − 3 is shown below. If the graph of the original function is shifted 5 units up, which of the following equations best represents the translation of each point on the curve?

Problem #36 Obj 5 - TAKS th [A.D2(B)] Which graph best represents an equation that has the roots x = and x = ½ ?

Problem #38 Obj 5 - TAKS th [A.D1(C)] The graph of a function of the form y = ax 2 + c is shown below. If the graph is translated only up or down to include the ordered pair (6, 7), which of the following equations best represents the resulting graph?