Graphing Properties

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?

2026 February(Z14) 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

A student modeled a set of paired data with the equation y = 0.25x + 80. The student's model and a scatterplot of the paired data are graphed in the given 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?

2026 April(R4A) 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

A system of equations, consisting of a quadratic equation and a linear equation, is graphed in the standard (x,y) coordinate plane as shown. One of the following lists only the point(s) whose coordinates are solutions to the system of equations. Which one?

2026 April(R4A) 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

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

The polynomial function graphed in the given standard (x,y) coordinate plane is an increasing function throughout one of the following intervals. Which one?

2026 April(R4A) Math Question 10

2012 June(70C) Math Question 11

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

The equations of four (x,y) relations are given below. I. 5y = (x − 1)(x − 3)(x + 3)  II. (x − 1)² + (y − 1)² = 9  III. y/4 = √(x + 4) − 1  IV. y + 5 = (2/5)ˣ. The graph in the standard (x,y) coordinate plane of each of these relations is shown below. Of these relations, which are functions?

2023 April(F11) Math Question 13

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

Let d be a function of t. The given graph of the function models the distance, d meters, left to hike on a trail t minutes since beginning the hike. It took a total of 13 minutes to hike the 860-meter trail. One of the following intervals is the domain of the function. Which one?

2025 October(J08) 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

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

Function f is an even function, which means the graph of y = f(x) is symmetric about the y-axis of the standard (x,y) coordinate plane. The graph of y = f(x) passes through the point (6,51). The graph must also pass through which of the following points?

2026 April(R4A) 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 December(71A) Math Question 18

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

Let f be the function defined by f(x) = (6√7)x / 2. The domain of f is the set of all real numbers. Which of the following sets is the range of f?

2026 April(R4A) 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

In the standard (x,y) coordinate plane, a certain dilation maps the point (0,0) to itself and maps the point (4,−16) to the point (1,−4). This dilation maps the point (12,−24) to the point:

2025 October(J08) 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

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

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. 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

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?

2026 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

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

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

Which of the following is the set of all possible values of t for which f(t) is defined?

2023 September(G01) 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

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

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

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

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

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

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

2013 December(71E) Math Question 34

2011 April(67F) Math Question 34

The function y = f(x) = 5/x is graphed in the standard (x,y) coordinate plane. One of the following statements is FALSE. Which one?

2024 June(G20) Math Question 35

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?

Graphing PropertiesThere are 185 ACT math questions under Graphing Properties

Sub-topics

2018 December(B05) Math Question 1

2026 February(Z14) Math Question 1