Graphing Properties

2018 December(B05) Math Question 1

2. In the standard (x,y) coordinate plane, point A has coordinates (−7,−5). Point A is translated 7 units to the left and 5 units down, and that image is labeled  A′. What are the coordinates of A ?

Translations

2021 April(D05) Math Question 2

2. A point at (-5,7) in the standard (x,v) coordinate plane is translated right 7 coordinate units and down 5 coordinate units. What are the coordinates of the point after the translation?

2019 June(A11) Math Question 2

2018 December(B05) Math Question 3

2010 December(69A) Math Question 3

2010 April(68G) Math Question 3

4. A group of students was surveyed about what types of music each had listened to during the previous week. Students could choose 1, 2, or 3 types of music (Rap, Rock, or Country), or they could respond "none of these music types." Only 10 students responded with "none of these music types," and 18 students responded that they had listened to all 3 types. In the figure below, the 8 regions show the numbers of responses in each category. One region had exactly 8 responses. W lat type(s) of music did those 8 students respond they had listened to during the previous week?

2016 December(74H) Math Question 4

5. What vector is the result of adding the vectors (1,-2), (2,3), and (-4,2) ?

2014 December(72G) Math Question 5

6. Portions of the graphs represented by the functions —2x + y = 2 and x + y = 5 are shown in the standard (x,y) coordinate plane below. Although only a portion of each graph is shown, the domain of each function is all real numbers. If it can be determined, at what point do the graphs intersect?

2016 December(74H) Math Question 6

2010 June(68C) Math Question 7

8.Two dials are shown below. When the arrow an each
dial is spun, it is equally likely to point at any of the
num.bered sectors on its dial after it has stopped
spinning. After the arrows ate next spun, the numbers
in the sectors the arrows point at after they stop
spinning will be added together.' Which of the
following values is NOT a possible sum of those
2 numbers?

2019 June(B02) Math Question 8

2020 June(C02) Math Question 8

2010 June(68C) Math Question 9

10. The fluctuation of water depth at a pier is shown in the figure below. One of the following values gives the positive difference, in feet, between the greatest water depth and the least water depth shown in this graph. Which value is it?

2017 April(74F) Math Question 10

10. Triangles nABC and nA′B′C′ are graphed in the standard (x,y) coordinate plane below. Triangle nA′B′C′ is the image of nABC under one of the following transformations. Which one?

Reflection

2020 December(D03) Math Question 10

2012 June(70C) Math Question 11

2012 April(70G) Math Question 11

12. What is the slope of HM, shown in the standard (x,y) coordinate plane below?

2016 December(74H) Math Question 12

14. A map of the locations of Marville, Sun Town, and Bright City is shown in the standard (x,y) coordinate plane below, where coordinates for x and y are given in miles. The coordinates of Marville and Bright City are given, and Sun Town is located along a straight line exactly halfway between Marville and Bright City. Highway H from Marville to Bright City is 390 miles long. Highway K from Sun Town to Bright City is 200 miles long. What are the coordinates of Sun Town?

2014 April(71H) Math Question 14

2011 June(69F) Math Question 14

14. The phrases below represent 3 types of measurements as functions of time. I. The height of an object falling toward the ground II. The height of a plant growing at a constant rate III. The distance a car travels while increasing its velocity Graphs A, B, and C below each represent one of these functions. For all graphs, the x-axis represents time. Which graph is of which function?

2016 April(73E) Math Question 14

2020 June(C02) Math Question 15

15. Two vectors are shown in the standard (x,y) coordinate plane below.

One of the following vectors in the standard (x,y) coordinate plane is the sum of these 2 vectors. Which one?

2021 June(D06) Math Question 15

2019 April(B04) Math Question 15

2019 December(C03) Math Question 16

16. The graph below shows the amount of water in,a pond
over a period of 7 hours. One of the following values is
the number of hours the amount of water in the pond
remained constant. Which one?

2019 June(B02) Math Question 16

16. Quadrant I of the standard (x,y) coordinate plane is shown on a large computer screen. A blinking dot is positioned at (2,3). The dot makes exactly 2 moves: first, horizontally in the positive x direction for 4 seconds at a speed of 0.5  coordinate units per second; then, vertically in the positive y direction for 2 seconds at the same speed. At what point is the dot located after these 2 moves?

2021 December(E23) Math Question 16

2012 June(70C) Math Question 17

2012 December(71A) Math Question 18

2012 April(70G) Math Question 18

20. Each side of a square is 3 cm long. One vertex of the square is at (4,2) on a square coordinate grid marked in centimeter units. Which of the following points on the grid could be another vertex of the square?

2014 December(72G) Math Question 20

2013 December(71E) Math Question 22

2011 June(69F) Math Question 22

22. Let a be positive and b be negative. If it can be determined, in which quadrant of the standard (x,y) coordinate plane is the point (−a,b2) located?

2021 June(D06) Math Question 22

2011 April(67F) Math Question 22

23. Given that the function f defined as f(x) = 5 - 3x has
domain { -1, 0,. 2}, what is the range off?

2019 June(B02) Math Question 23

23. In the standard (x,y) coordinate plane, a translation maps a point (x,y) to its image (x — 5, y + 3). To what image does this translation map (-3,-2) ?

2016 December(74H) Math Question 23

2013 December(71E) Math Question 23

2019 April(B04) Math Question 23

2012 December(71A) Math Question 23

23. Given y = x /(x-1) and x > 1, which of the following is apossible value of y ?

Domain and Range

2021 April(Z04) Math Question 23

2013 December(71E) Math Question 24

24. The graph in the standard (x,y) coordinate plane below is represented by one of the following equations. Which equation?

2018 June(A11) Math Question 24

2010 April(68G) Math Question 24

25. The point (6,3) and the line y = 7 are graphed in the standard (x,y) coordinate plane below. After the point has been reflected across the line, what are the coordinates of the point's image?

2015 December(72E) Math Question 25

25. What score will Halle need to earn in her 3rd game to have an average score of 172 for the 3 games?

2017 December(A10) Math Question 25

25. Lyman has plotted 5 points in the standard (.v,y) coordinate plane below. He then plots a new point as follows: the x-coordinate of the new point is the mean of the .v-coordinates of the 5 points already plotted; the y-coordinate of the new point is the mean of the y-coordinates of the 5 points already plotted. Which of the following ordered pairs gives the coordinates of Lyman’s new point?

2018 April(A09) Math Question 25

2013 April(71G) Math Question 26

2010 December(69A) Math Question 26

27. The entire graph of the relation R of the ordered pairs (x,y) is shown in the standard (x,y) coordinate plane below. One of the following sets is the domain of the relation R. Which set is it?

2016 April(73E) Math Question 27

2009 December(68A) Math Question 29

29. The number a is located at —2.5 on the number line below.

2017 April(74F) Math Question 29

2019 April(Z15) Math Question 29

30. The equation y = :2+-34 is graphed in the standard (x,y) coordinate plane below. No point on the graph has which of the following x-coordinates?

2013 June(71C) Math Question 30

31. In the standard (x,y) coordinate plane below, ABC
will be translated 10 units down and then the resulting ,
image will be reflected over the y-axis. What will be
the coordinates of the final image of A resulting from
both transformations?

2019 June(B02) Math Question 31

31. The vector i represents 1 mile per hour east, and the vector  j represents 1 mile per hour north. Maria is jogging south at 12 miles per hour. One of the following vectors represents Maria’s velocity, in miles per hour. Which one?

Components of a Vector

2021 April(Z04) Math Question 31

32. The circle will be reflected across the y-axis. What will be the coordinates of the image of the center of the circle?

2015 April(73G) Math Question 32

32. Parallelogram ABCD will be reflected over the y-axis. What will be the coordinates of the image of A ?

2017 June(74C) Math Question 32

2019 December(C03) Math Question 32

32. A series of transformations are applied to the graph in the standard (x,y) coordinate plane below. The graph below is reflected across the x-axis. The new graph is reflected across the y-axis. This new graph is rotated 90° clockwise ( ) about the origin. The resulting graph is one of the following graphs. Which one?

2020 December(D03) Math Question 32

33. A function is defined by g(a) = —2a +7, and its domain is the set of integers from 1 through 30. inclusive. For how many values of a is g(a) negative?

2015 December(72E) Math Question 33

33. In the standard (x,y) coordinate plane, A’ is the image resulting from the reflection of the point A(2,-3) across the y-axis. What are the coordinates of A’ ?

2018 June(A11) Math Question 33

33. The plan of the garden will be aligned in the standard (x,y) cdordinate plane so that the right angle is at (0,0) and the other 2 vertices are at (12,0) and (0,-9). What coordinates give the location of the water sprinkler?

2014 December(72G) Math Question 33

2019 April(B04) Math Question 33

2009 June(67C) Math Question 33

2013 December(71E) Math Question 34

2011 April(67F) Math Question 34

36. Consider the graph of the equation y = 3x in the 2x — 6 standard (x,y) coordinate plane. Which of the following equations represents the vertical asymptote of the graph?

2018 June(A11) Math Question 36

36. The figure will be placed in the standard (x,y) coordinate plane so that K is at the origin, AB is parallel to the x-axis, and 1 meter equals 1 coordinate unit. Which of the following values could be the y-coordinate of H?

2015 June(73C) Math Question 36

36. The rental fee for the use of a reception hall is $500. To encourage use of the hall’s catering service, the hall’s rental fee is reduced by $100 for each group of 20 meals ordered through the hall’s catering service. All 20 meals in a group must be ordered for each reduction in the rental fee. One of the following graphs shows the hall’s rental fee when 0 to 100 meals are ordered. Which graph is it?

2014 April(71H) Math Question 36

2019 June(72F) Math Question 37

37. What is the length, in coordinate units, of the altitude from C to AB in ABC shown in the standard (x, y) coordinate plane below?

2015 June(73C) Math Question 37

2018 December(B05) Math Question 37

2019 April(B04) Math Question 37

38. In the standard (x,y) coordinate plane below, a circle has a radius of r coordinate units and passes through the origin, O. The circle has diameter OS, where S lies on the negative y-axis. In terms of r, what are the coordinates of S ?

2015 December(72E) Math Question 38

2019 June(72F) Math Question 38

2013 April(71G) Math Question 38

2012 December(71A) Math Question 38

2018 December(B05) Math Question 38

2010 April(68G) Math Question 38

2013 April(71G) Math Question 40

2010 April(68G) Math Question 40

40. Regardless of how the graph is oriented in the standard (x,y) coordinate plane, NO graph in one of the following categories has a vertical line of symmetry. Which one?

Lines of Symmetry

2021 April(Z04) Math Question 40

41. A Ferris wheel is turning at a constant speed during 1 of its rotations. Let t represent the time that has elapsed since the wheel started turning and let h represent the height above ground level of a certain seat on the wheel. The seat is at its minimum height at t = a seconds and is at its maximum height at t = b seconds. One of the following graphs represents the relationship between t and h during this rotation. Which one?

2013 June(71C) Math Question 41

41. When the vector ai + 3j is added to the vector —2i + bj, the sum is 61 — 6j. What are the values of a and b ?

2018 June(A11) Math Question 41

41. When ABCD is reflected over the y-axis to A'B'C'D', what are the coordinates of D'?

2014 June(72C) Math Question 41

2019 June(72F) Math Question 42

2020 June(C02) Math Question 42

2010 June(68C) Math Question 43

2009 June(67C) Math Question 43

2020 June(C02) Math Question 43

44. Right triangle RST will be rotated about the x-axis to form a right circular cone. How long, in coordinate units, is the radius of the cone's base?

2015 December(72E) Math Question 44

2009 June(67C) Math Question 44

2019 June(72F) Math Question 45

46. When graphed in the standard (x,y) coordinate plane, the lines x = —3 and y = x — 5 intersect at what point?

2015 December(72E) Math Question 46

46. The difference  3/5 - (-1)/3 lies in which of the following
intervals graphed on the real number line?

2019 June(B02) Math Question 46

2019 April(B04) Math Question 46

2010 April(68G) Math Question 46

46. The points graphed in the standard (x,y) coordinate plane below show the positions of 5 stars in a plane relative to a point represented by the origin, where each coordinate unit equals 1 light-year. A light-year is the distance that light travels in 1 year, and 1 light-year 5.9 x 1012 miles. The distance from Star A to Star D is approximately 11.4 light-years. Star A has a mass of 3 solar masses; and Stars B, C, D, and E each have a mass of 1 solar mass. Because Stars B, C, D, and E have the same mass, the position determined by the average of the x-coordinates and the average of the y-coordinates of those stars approximates the center of mass of those 4 stars. What are the coordinates of this position?

Graphing PropertiesThere are 138 ACT math questions under Graphing Properties

Sub-topics

2018 December(B05) Math Question 1

2021 April(D05) Math Question 2