Continuity Quizzes, Questions & Answers

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Continuous Functions Quizzes

Definition Mastery Quiz on Subspace and Induced Topology

Think you can keep all the subspace definitions straight? This quiz focuses on the precise definitions behind the induced topology. You’ll check your understanding of how ope...

Questions: 15 | Attempts: 10 | Last updated: Dec 19, 2025

Sample Question
If Y⊆X, the induced topology on Y always contains fewer open sets than the topology of X.

True

False

Fundamentals of Continuity: Limits, One-Sided Limits, and Function Behavior

Think you can handle the formal rules behind induced topology? This quiz guides you through the core definitions: how open and closed sets in a subspace are formed, what happens wh...

Questions: 15 | Attempts: 10 | Last updated: Dec 15, 2025

Sample Question
If a function is continuous at every point of its domain, it must also be continuous on any subset of its domain.

True

False

Applied Continuity Quiz: Real-World Functions and Limit Reasoning

Ready to spot induced topology outside the classroom? This quiz shows how restricting attention to smaller regions — like a building, a city district, a race track, or a coas...

Questions: 15 | Attempts: 10 | Last updated: Dec 15, 2025

Sample Question
If a car’s position s(t) is continuous, what real-world fact does this represent?

Car teleports

Moves without jumps

Must be constant speed

Car cannot stop

All Continuous Functions Quizzes

Epsilon Delta Proofs Quizzes

Foundations of Epsilon–Delta Proofs Quiz

Think you understand the ε–δ definition of limits and continuity? This quiz helps you apply the formal framework behind limits, piecewise continuity, and &delta...

Questions: 15 | Attempts: 12 | Last updated: Dec 12, 2025

Sample Question
If |x−a| < δ implies |f(x)−L| < ε, then the limit exists and equals L.

True

False

Practice with Epsilon–Delta Proofs Quiz

Ready to apply ε–δ reasoning to a variety of functions? This quiz gives you hands-on practice with the limit definition using deleted neighborhoods, bounding te...

Questions: 15 | Attempts: 12 | Last updated: Dec 12, 2025

Sample Question
Which statements correctly express the ε–δ definition of limit?

For every ε > 0, there exists δ > 0

If 0 < |x − a| < δ, then |f(x) − L| < ε

F(a) must equal L for the limit to exist

δ depends on ε

Epsilon–Delta Continuity Quiz

Ready to practice the formal definition of continuity? This quiz helps you understand how ε–δ arguments connect input closeness to output closeness. You'll ...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
If a function is continuous at a, then for every ɛ>0, there exists a δ>0 such that whenever |x−a|<δ, we have |f(x)−f(a)|<ɛ.

True

False

All Epsilon Delta Proofs Quizzes

Topological Continuity Quizzes

Topological Continuity Quiz

Ready to understand continuity beyond ε–δ definitions? This quiz introduces the topological definition of continuity, where open sets and their preimages determ...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
In topology, a function is continuous if the preimage of every open set is open.

True

False

Topological Continuity Concepts Quiz

Think you understand topological continuity? This quiz explores the formal definition using preimages of open sets and examines how continuity behaves in discrete, trivial, and gen...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
Which of the following is the correct topological definition of continuity of f : X → Y?

Images of open sets are open

Preimages of open sets are open

Images of closed sets are closed

Preimages of compact sets are compact

Applying Topological Continuity Quiz

How well can you apply the topological definition of continuity? This quiz helps you connect theory to practice by examining preimages of open sets, behavior on basis elements, con...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
A function f : X → Y is continuous if:

The preimage of every open set in Y is open in X.

The preimage of every closed set in Y is closed in X.

For each x ∈ X, the function preserves neighborhood structure.

F is injective.

All Topological Continuity Quizzes

Discontinuous Functions Quizzes

Applying Discontinuity Concepts Quiz

How well can you apply discontinuity concepts to real functions? This quiz guides you through analyzing limits, evaluating undefined points, and classifying different types of disc...

Questions: 15 | Attempts: 11 | Last updated: Dec 12, 2025

Sample Question
A function f is discontinuous at a if:

F(a) does not exist

Lim f(x) does not exist

Lim f(x) != f(a)

F is differentiable at a

Discontinuous Functions Quiz

Ready to understand how and why functions break continuity? This quiz introduces you to the different types of discontinuities—removable, jump, infinite, and oscillatory&mdas...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
A function can be discontinuous at more than one point.

True

False

Discontinuity Types and Behavior Quiz

Think you can spot discontinuities quickly? This quiz challenges you to identify when a function is discontinuous and what type of discontinuity it has. You’ll analyze behavi...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
Which of the functions has a removable discontinuity at x = 2?

F(x) = x^2 - 4

F(x) = 1/(x-2)

F(x) = ⌊x⌋

F(x) = tan(x)

All Discontinuous Functions Quizzes

Top Trending Continuity Quizzes

Math Quiz: Limits And Continuity Practice Test

When it comes to calculus, a limit is described as a number that a function approaches as the independent variable of the function approaches a given value. On the other hand, a continuity is reflected on a graph illustrating a...

Questions: 10 | Attempts: 2723 | Last updated: Mar 22, 2025

Sample Question
In the function f(x)=3x, what is the limit of f(x) as x approaches 2?

3

6/2

6

6/3

Connections Between Function Features And Limits

What does different limits information tell us about the features of a function?

Questions: 5 | Attempts: 478 | Last updated: Mar 20, 2025

Sample Question
Select all the places to look for extreme points (maxima, minima):

Where the instantaneous rate of change is zero

Where the instantaneous rate of change does not exist

At the endpoints of the interval of interest

Where the function value is zero

Math Quiz: Take The Limits And Continuity Assessment Test

A limit is a number that a function approaches as the autonomous variable of the function approaches a given value. Take this assessment test to evaluate your insight.

Questions: 10 | Attempts: 181 | Last updated: Mar 21, 2025

Sample Question
Evaluate the limit ( x – 4 ) / (x2 – x – 12) as x approaches 4.

0

Infinity

1/7

Undefined

Limits And Continuity Test! Calculus Trivia Questions Quiz

Calculus Trivia Questions Quiz is on Limits and Continuity. If you want to have an easy time when it comes to calculus, you need to understand the concepts of limits, and you are in luck as the quiz below will help you do just...

Questions: 12 | Attempts: 245 | Last updated: Mar 21, 2025

Sample Question
Select the most appropriate option.

A

B

C

D

Recent Continuity Quizzes

Limits Language, Notation, And Features Of Functions

Limits Language, Notation, and Features of Functions

Check your basic knowledge: limits language and notation types of discontinuities asymptotes and end behavior

Questions: 15 | Attempts: 816 | Last updated: Mar 19, 2025

Sample Question
What feature(s) are described by the limit(s) information below? Check all that apply.

Essential discontinuity

Jump discontinuity

Removable discontinuity

End behavior

Horizontal asymptote

Vertical asymptote

AP Calculus Test: Limits And Continuity!

AP Calculus Test: Limits and Continuity!

AP calculus test: Limits and Continuity is an integral part of high school and college mathematics. Engineering students and other students of mathematics, including physics and chemistry, also use it in solving problems. This...

Questions: 10 | Attempts: 543 | Last updated: Mar 22, 2025

Sample Question
The mean value of a Sine wave over half a cycle is:

0.318 × maximum value

0.707 × maximum value

The peak value

0.637 × maximum value

Continuity Quizzes, Questions & Answers

Popular Continuity Topics

Continuous Functions Quizzes

Epsilon Delta Proofs Quizzes

Topological Continuity Quizzes

Discontinuous Functions Quizzes

Top Trending Continuity Quizzes

Recent Continuity Quizzes