AP Calculus AB Practice Quiz: Estimating Limit Values from Graphs
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 11 questions to check your progress.
Question 1 of 11
All Questions (11)
A) 0
B) 2
C) 4
D) Does not exist
Correct Answer: C
To estimate the limit of f(x) as x approaches 2, we examine the y-value the function approaches from both the left and the right of x=2. As x gets closer to 2 from either side, the graph shows that the y-value gets closer to 4. Therefore, the limit is 4.
A) -1
B) 3
C) 1
D) Does not exist
Correct Answer: B
The limit of a function as x approaches a value is the y-value that the function gets closer to from both sides. As x approaches -1 from both the left and the right, the graph of g(x) approaches the y-value of 3. The existence of a hole at (-1, 3) does not affect the value of the limit.
A) -1
B) 1
C) 2
D) Does not exist
Correct Answer: C
The notation x→1⁻ indicates the limit as x approaches 1 from the left side (i.e., for values of x less than 1). Following the graph from the left towards x=1, the function's y-value approaches 2.
A) -1
B) 1
C) 2
D) Does not exist
Correct Answer: A
The notation x→1⁺ indicates the limit as x approaches 1 from the right side (i.e., for values of x greater than 1). Following the graph from the right towards x=1, the function's y-value approaches -1.
A) h(1) is defined.
B) The function approaches infinity at x=1.
C) The function is not continuous at x=1.
D) lim(x→1⁻) h(x) ≠ lim(x→1⁺) h(x)
Correct Answer: D
A limit exists at a point c if and only if the left-sided limit equals the right-sided limit. From the graph, the limit from the left is 2 and the limit from the right is -1. Since these one-sided limits are not equal, the overall (two-sided) limit does not exist. While it's true the function is not continuous (Option C), the reason the limit fails to exist is the disagreement between the one-sided limits.
A) 0
B) 3
C) +∞
D) Does not exist
Correct Answer: D
As x approaches 3 from both the left and the right, the function's value increases without bound. Because the function does not approach a specific, finite real number, the limit does not exist. While we can describe the behavior as tending towards infinity, the formal limit does not exist.
A) lim(x→-1) f(x) = 1 and f(-1) = 3
B) lim(x→-1) f(x) = 3 and f(-1) = 1
C) lim(x→-1) f(x) = 1 and f(-1) = 1
D) lim(x→-1) f(x) does not exist and f(-1) = 1
Correct Answer: B
The limit is the value the function approaches as x gets close to -1. From the graph, the function approaches the y-value of the hole, which is 3. The function value, f(-1), is the y-coordinate of the solid dot at x=-1, which is 1. Therefore, lim(x→-1) f(x) = 3 and f(-1) = 1.
A) One-sided limits are impossible to determine from a graph.
B) The graph can only show rational function values.
C) The scale of the viewing window may hide a small hole or jump, making a discontinuous function appear continuous.
D) Graphs cannot be used to estimate limits that are infinite.
Correct Answer: C
A key limitation of using graphical representations is the issue of scale. A viewing window might not have the resolution to show very small-scale behavior. A tiny hole (removable discontinuity) or a very small jump might be missed, leading to the incorrect conclusion that the function is continuous and that the limit equals the function's apparent value.
A) 1
B) -2
C) The limit is the same as k(-2).
D) Does not exist
Correct Answer: D
For a two-sided limit to exist, both the left-sided and right-sided limits must exist and be equal. Since the function k is not defined for x < -2, the left-sided limit lim(x→-2⁻) k(x) does not exist. Because one of the one-sided limits does not exist, the overall two-sided limit does not exist.
A) 2
B) -1
C) The average of the left and right limits.
D) Does not exist
Correct Answer: D
The limit of g(x) as x approaches 1 exists only if the limit from the left equals the limit from the right. From the graph, lim(x→1⁻) g(x) = 2 and lim(x→1⁺) g(x) = -1. Since 2 ≠ -1, the two-sided limit does not exist.
A) lim(x→0) p(x) = +∞
B) lim(x→0) p(x) = -∞
C) lim(x→0) p(x) does not exist because the one-sided limits describe different unbounded behavior.
D) lim(x→0) p(x) = 0
Correct Answer: C
The limit does not exist. As x approaches 0 from the left, the function increases without bound (approaches +∞). As x approaches 0 from the right, the function decreases without bound (approaches -∞). Because the left-sided and right-sided limits do not agree (and are not finite), the overall limit does not exist. Option C provides the most precise reason.