Graphing Properties

Interpret Graphs or Figures

2018 December(B05) Math Question 1

A point at (−4,10) in the standard (x,y) coordinate plane is translated right 10 coordinate units and down 4 coordinate units. What are the coordinates of the point after the translation?

35 February(Z14) Math Question 1

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

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

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

A rhombus is a quadrilateral with all 4 sides of equal length. Three vertices of a rhombus are graphed in the standard (x,y) coordinate plane below. One of the following points is the location of the 4th vertex of this rhombus. Which one?

2023 April(F11) Math Question 10

2012 April(70G) Math Question 11

A student modeled a set of paired data with the equation y = 0.25x + 25. The student's model and a scatterplot of the paired data are graphed in the standard (x,y) coordinate plane. Among the following possible changes to the student's equation, which one will most improve the fit to the paired data?

2025 October(J08) Math Question 11

One of the lines graphed in the standard (x,y) coordinate plane below has a negative slope and a negative y-intercept. Which one?

2024 September(H11) 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

A section of highway is represented by a line segment with endpoints (30,50) and (90,100) in the standard (x,y) coordinate plane. Exactly halfway along this highway section is a road sign. What are the coordinates of the road sign?

2024 April(Z13) Math Question 14

2020 June(C02) Math Question 15

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

2012 June(70C) Math Question 17

A circle with the equation x² + y² = 36 is graphed in the standard (x,y) coordinate plane. At what points does the circle intersect the x-axis?

2024 December(H31) Math Question 17

2012 April(70G) Math Question 18

A circle with the equation x² + y² = 16 is graphed in the standard (x,y) coordinate plane. At what points does the circle intersect the x-axis?

2024 April(Z13) 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 April(67F) Math Question 22

Points G(2,6) and H(10,14) lie in the standard (x,y) coordinate plane. What is the midpoint of GH?

2024 September(H11) Math Question 22

2013 December(71E) Math Question 23

2019 April(B04) 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

Kate is going to buy meat (beef and chicken) for a party. Beef costs $3.00 per pound, chicken costs $2.00 per pound, and Kate has a budget of $90.00 to spend on meat for the party. The shaded region in one of the following graphs represents all and only the possible combinations of beef and chicken Kate can buy while staying within her budget. Which one?

2024 June(G20) Math Question 24

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

Trapezoid A and Trapezoid B are congruent and graphed in the standard (x,y) coordinate plane below. One of the following transformations or sequences of transformations would map Trapezoid A onto Trapezoid B. Which one?

2024 September(H11) Math Question 25

2013 April(71G) Math Question 26

2010 December(69A) Math Question 26

Rate of change is defined to be the vertical change between any 2 points divided by the horizontal change between the same 2 points. A function containing the point (0,1) has a constant rate of change equal to 3/2. The function is shown in one of the standard (x,y) coordinate plane graphs below. Which one?

35 February(Z14) Math Question 26

A circle with its center at (5,4) and a radius of 3 coordinate units is graphed in the standard (x,y) coordinate plane. One point on the circle has a y-coordinate greater than that of any other point on the circle. What is the y-coordinate of that point?

2024 September(H11) Math Question 26

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

2017 April(74F) Math Question 29

Dai traveled to 3 locations during a workday. Dai remained at each location a whole number of hours. The graph below shows the relationship between time, in hours, into his workday and total distance, in miles, traveled. Which of the following values is closest to Dai's average speed, in miles per hour, for the parts of the workday when he was traveling?

2023 April(F11) Math Question 29

In the figure below, 5 right triangles share a common vertex, O. The legs of each of these triangles are shown dashed, and their lengths are labeled in feet. The point on each triangle that is farthest from O is labeled A, B, C, D, or E. A circle centered at O with a radius of 10 feet will be drawn. Which of the following points is outside of this circle?

2024 September(H11) Math Question 29

In order to obtain the graph of a new function, g(t), the graph of f(t) is translated 2 units to the right and then reflected over the x-axis. The point (1,90) on the graph of f(t) corresponds to what point on the graph of g(t)?

2023 September(G01) Math Question 30

The graph in the standard (x,y) coordinate plane below has 5 lines of symmetry that all intersect at the origin. What is the smallest positive clockwise rotation about the origin that can be applied to this graph with the result being this graph?

2024 June(G20) Math Question 32

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

2009 June(67C) Math Question 33

Rectangle EFGH with vertices at (−1,3), (2,3), (2,−1), and (−1,−1) is shown in the standard (x,y) coordinate plane below. The quadrants of the coordinate plane are labeled. What percent of the rectangle's area lies in Quadrant IV?

2024 December(H31) Math Question 33

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

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

2010 April(68G) Math Question 38

2019 June(72F) Math Question 42

2020 June(C02) Math Question 42

Which of the following points is NOT on the graph of the function y = |2x| − 4 in the standard (x,y) coordinate plane?

2023 September(G01) Math Question 42

2009 June(67C) Math Question 43

2020 June(C02) Math Question 43

Vector AB is shown in the standard (x,y) coordinate plane below. Point C will be placed on AB so that AC = 1/4 AB. What will be the coordinates of point C?

2023 September(G01) Math Question 45

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?

2016 April(73E) Math Question 46

48. ABC Cabs and Tary Taxicabs both have an initial fare of a whole number of dollars for 1 passenger. The fare increases a whole number of dollars at each whole number of miles traveled. The graphs below show the 1-passenger fares, in dollars, for both cab companies for trips up to 6 miles. When the fares of the 2 cab companies are compared, what is the cheaper fare for a 5-mile trip?

2017 April(74F) Math Question 48

In the standard (x,y) coordinate plane, the graph of y = 5x² is reflected over the x-axis and then translated to the right 3 coordinate units. The graph of which of the following equations is the result of these 2 transformations?

2024 September(H11) Math Question 49

2009 June(67C) Math Question 50

The graph in the standard (x,y) coordinate plane of y = a(x − b)², where |a| ≠ |b|, is reflected across the x-axis. Which of the following is an equation of the reflection?

35 February(Z14) Math Question 50

One of the following is a hyperbola graphed in the standard (x,y) coordinate plane. Which one?

2024 December(H31) Math Question 51

2009 June(67C) Math Question 52

How many periods does the pump complete in 1 hour?

2024 June(G20) Math Question 52

2019 April(Z15) Math Question 53

One of the following values is the volume, in gallons, of water in the tank after 51 seconds. Which one?

2024 June(G20) Math Question 53

2010 June(68C) Math Question 54

56. The function f (x) is shown below with several points
labeled. Another function, g(x), is defined such that
g(x) = --[f(x) - 3].   What is g(4)?

2019 June(B02) Math Question 56

2009 April(66F) Math Question 56

Rectangle ABCD is graphed in the standard (x,y) coordinate plane below. Rectangle ABCD undergoes a dilation with a center of A and a scale factor of 3/2. One of the following is the graph of the image of rectangle ABCD under this dilation. Which one?

2024 December(H31) Math Question 56

The ellipse in the standard (x,y) coordinate plane below is centered at the origin. The endpoints of the major and minor axes of the ellipse are labeled. Which of the following equations determines this ellipse?

Interpret Graphs or FiguresGraphing PropertiesACT math questions

2018 December(B05) Math Question 1

35 February(Z14) Math Question 1