Graphing Properties

Domain, Range, Asymptote, Undefined

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

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

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

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. 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

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

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

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

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

2013 December(71E) 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

For what value of x, if any, is the function below undefined? f(x) = (−1)(x + 2)/(x + 2)

2024 December(H31) Math Question 37

2018 December(B05) Math Question 38

The domain of the real-valued function f(x) = 2/√(x − 3) is the set of all x-values that satisfy:

35 February(Z14) Math Question 38

What are the equations of all the asymptotes in the standard (x,y) coordinate plane for the function y = f(x) = 3x²/(x² − 9)?

2025 October(J08) Math Question 41

2010 June(68C) Math Question 43

A relation pairs elements in the domain with elements in the range. The table below defines a relation where the domain is represented by the x-values and the range is represented by the y-values. Which of the following statements indicates whether this relation is a function of x and provides a valid reason?

2024 April(Z13) Math Question 44

Consider the function f defined by f(x) = −(1/3)x − 5 with domain −6 ≤ x ≤ 9. What is the range of f?

2024 December(H31) Math Question 46

47. The domain of f(x) = 2/(x^3-9x) is the set of all real numbers EXCEPT:

2015 April(73G) Math Question 47

48. The expression 2b + c b — 2c is undefined whenever b = ?

2018 April(A09) Math Question 48

2019 June(72F) Math Question 49

49. In the standard (x,y) coordinate plane, for what value(s) of x, if any, is there NO value of y such that (x,y) is on the graph of y = (x - 3)/(x + 3)(x + 2)(x - 2)?

2016 April(73E) Math Question 49

50. The graph of f(x) 2 X- 3 is shown below. What is

2017 June(74C) Math Question 50

2013 April(71G) Math Question 50

2020 June(C02) Math Question 51

52. At what point in the standard (x,y) coordinate plane do

2016 December(74H) Math Question 52

Let a, b, c, and d be real numbers greater than or equal to 2. Four functions are listed below. f(x) = ab^x, g(x) = ax + b, h(x) = ax² + bx + c, k(x) = ax³ + bx² + cx + d. The values of which of the listed functions will exceed the values of all the other listed functions as x approaches infinity?

2024 December(H31) Math Question 52

2012 April(70G) Math Question 54

For all negative values of k, what is the range of values of 2^k?

2024 April(Z13) Math Question 54

2011 April(67F) Math Question 56

2010 June(68C) Math Question 57

58. The entire graph of y =f(x) is shown in the standard (x,y) coordinate plane below. One of the following sets is the domain off. Which set?

2013 June(71C) Math Question 58

59. Which of the following linear equations gives the vertical asymptote for the graph of y = 201x+ 202 / 203x + 204 in the standard (x,y) coordinate plane?

2015 June(73C) Math Question 59

Which of the following degree values of x is NOT in the domain of the function below? f(x) = 1/(1 + sec x)

2024 April(Z13) Math Question 59

60. The equation y = (2x^2-18)/(X^2— 5x) has 2 vertical asymptotes and 1 horizontal asymptote. What is the horizontal asymptote?

2015 April(73G) Math Question 60

The graph of f(x) is shown in the standard (x,y) coordinate plane below. The graph of f(x) has horizontal asymptotes at y = −2 and y = 2. One of the following intervals represents the domain of f⁻¹(x). Which one?

Domain, Range, Asymptote, UndefinedGraphing PropertiesACT math questions

2023 April(F11) Math Question 13

2025 October(J08) Math Question 14