Applying Discontinuity Concepts Quiz

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7288 | Total Attempts: 9,526,234
| Questions: 15 | Updated: Nov 24, 2025
Please wait...
Question 1 / 15
0 %
0/100
Score 0/100
1) A function f is discontinuous at a if:

Explanation

Discontinuous if value missing, limit missing, or mismatch.

Submit
Please wait...
About This Quiz
Applying Discontinuity Concepts Quiz - 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 discontinuities. You’ll work with rational expressions, trigonometric functions, oscillatory functions, and piecewise-defined functions to determine what kind of discontinuity occurs and why. Through these examples,... see moreyou’ll learn how discontinuities arise and when redefining a function can make it continuous. By the end, you’ll be able to identify and explain discontinuities in a wide range of functions with confidence! see less

2)
You may optionally provide this to label your report, leaderboard, or certificate.
2) Which is a property of removable discontinuity?

Explanation

Removable: limit exists but value wrong/missing.

Submit
3) A jump discontinuity occurs when:

Explanation

Jump: finite unequal one-sided limits.

Submit
4) Infinite discontinuities occur when:

Explanation

Infinite: vertical asymptote.

Submit
5) Oscillatory discontinuities occur when:

Explanation

Oscillation prevents limit.

Submit
6) For f(x)=(x^2-1)/(x-1):

Explanation

Simplifies to x+1 except at 1.

Submit
7) Consider f(x)=1/|x| at x=0:

Explanation

1/|x|→∞.

Submit
8) For f(x)=tan(x), discontinuities at:

Explanation

tan undefined when cos=0.

Submit
9) Which functions are discontinuous at 0?

Explanation

1/x infinite; floor jump; sin1/x oscillatory.

Submit
10) Typical rational hole problem:

Explanation

Standard removable hole.

Submit
11) If infinitely many jump discontinuities on (0,1):

Explanation

Dense jumps but integrable if measure zero.

Submit
12) For f(x)=1/(x-1) at x=1:

Explanation

1/(x-1)→∞.

Submit
13) Discontinuity of 1/(x^2-9) at x=3:

Explanation

Denominator zero → asymptote.

Submit
14) For f(x)=|x|/x:

Explanation

Sign function jumps.

Submit
15) Which are discontinuous on measure-zero set?

Explanation

Dirichlet is not measure-zero.

Submit
View My Results
Cancel
  • All
    All (15)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
A function f is discontinuous at a if:
Which is a property of removable discontinuity?
A jump discontinuity occurs when:
Infinite discontinuities occur when:
Oscillatory discontinuities occur when:
For f(x)=(x^2-1)/(x-1):
Consider f(x)=1/|x| at x=0:
For f(x)=tan(x), discontinuities at:
Which functions are discontinuous at 0?
Typical rational hole problem:
If infinitely many jump discontinuities on (0,1):
For f(x)=1/(x-1) at x=1:
Discontinuity of 1/(x^2-9) at x=3:
For f(x)=|x|/x:
Which are discontinuous on measure-zero set?
Alert!

Advertisement