Is the function continuous at x = 2, and why?

No, $$\lim_{x\rightarrow2^-}f\left(x\right)\ne\lim_{x\rightarrow2^+}f\left(x\right)$$

Yes, $$\lim_{x\rightarrow2}f\left(x\right)=f\left(2\right)$$

Yes, $$\lim_{x\rightarrow2^-}f\left(x\right)=\lim_{x\rightarrow2^+}f\left(x\right)$$

No, $$\lim_{x\rightarrow2}f\left(x\right)\ne f\left(2\right)$$

Is f(x) continuous at x = a, and why?

No, $$\lim_{x\rightarrow a}f\left(x\right)\ne f\left(a\right)$$

No, $$\lim_{x\rightarrow a^-}f\left(x\right)\ne\lim_{x\rightarrow a^+}f\left(x\right)$$

Yes, $$\lim_{x\rightarrow a^-}f\left(x\right)=\lim_{x\rightarrow a^+}f\left(x\right)$$

Yes, $$\lim_{x\rightarrow a}f\left(x\right)=f\left(a\right)$$

Use the definition of continuity to determine whether the function is continuous at x = 7.

No, it's not continuous because the limit does not exist as x approaches 7.

No, it's not continuous because the function is not defined at x = 7.

No, it's not continuous because the value at x = 7 does not equal the limit.

The graph of the function f is shown. Which of the following statements is FALSE?

lim ⁡ x → 4 f ( x ) \lim_{x\rightarrow4}f\left(x\right) x → 4 lim f ( x ) exists

lim ⁡ x → 2 f ( x ) \lim_{x\rightarrow2}f\left(x\right) x → 2 lim f ( x ) exists

lim ⁡ x → 3 f ( x ) \lim_{x\rightarrow3}f\left(x\right) x → 3 lim f ( x ) exists

lim ⁡ x → 5 f ( x ) \lim_{x\rightarrow5}f\left(x\right) x → 5 lim f ( x ) exists

The function f is continuous at x=3

The graph of a function f is shown in the figure above. Which of the following statements is true?

lim ⁡ x → a f ( x ) = 2 \lim_{x\rightarrow a}f\left(x\right)=2 x → a lim f ( x ) = 2

f ( a ) = 2 f\left(a\right)=2 f ( a ) = 2

lim ⁡ x → a f ( x ) = 1 \lim_{x\rightarrow a}f\left(x\right)=1 x → a lim f ( x ) = 1

lim ⁡ x → a f ( x ) \lim_{x\rightarrow a}f\left(x\right) x → a lim f ( x ) does not exist

Which of the following best describes the continuity at x = 5?

Non-removable Infinite Discontinuity

Non-removable Jump Discontinuity

Classify the function as continuous or classify its discontinuity.

Discontinuous with a jump discontinuity

Discontinuous with a removable discontinuity

Discontinuous with an infinite discontinuity

Which of the following must be true for a function to be continuous at a point, a? (select all that apply)

the limit as x approaches a must exist

f(a) and the limit as x approaches a must be equal

the function has to go to infinity

you won't need to do any factoring/simplifying when finding the limit

Final Review on Limits and Continuity

Authored by Solomon Abalaka

Mathematics

12th Grade

Used 2+ times

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

Content View

Student View

30 questions

Show all answers

MULTIPLE CHOICE QUESTION

1 min • 1 pt

-2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

I and II, only

II and III, only

II, only

I, II, and III

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

-1

DNE

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

-1

DNE

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

-1

DNE

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

-2

-4

DNE

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

-2

-4

DNE

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

25 questions

Simplify Rational Exponents

Quiz

•

10th - 12th Grade

25 questions

Grade 8 November CP : Mensuration

Quiz

•

8th Grade - University

25 questions

final review

Quiz

•

8th Grade - University

25 questions

Squares Rhombi Properties

Quiz

•

9th - 12th Grade

25 questions

Exponent Rules and Simplifying Radicals

Quiz

•

9th - 12th Grade

25 questions

Circle Formulas Review

Quiz

•

9th - 12th Grade

25 questions

Cubic Functions Graphing and Evaluating

Quiz

•

9th - 12th Grade

30 questions

add

Quiz

•

5th - 12th Grade

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

14 questions

Boundaries & Healthy Relationships

Lesson

•

6th - 8th Grade

13 questions

SMS Cafeteria Expectations Quiz

Quiz

•

6th - 8th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

12 questions

SMS Restroom Expectations Quiz

Quiz

•

6th - 8th Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

10 questions

Pi Day Trivia!

Quiz

•

6th - 9th Grade

Discover more resources for Mathematics

15 questions

Pi Day Trivia

Quiz

•

9th - 12th Grade

25 questions

PI Day Trivia Contest

Quiz

•

9th - 12th Grade

20 questions

Pi Day

Quiz

•

6th - 12th Grade

20 questions

Solve Polynomials and Factoring Problems

Quiz

•

9th - 12th Grade

15 questions

Exponential Growth and Decay Word Problems Practice

Quiz

•

9th - 12th Grade

37 questions

A.7C - Quadratic Transformations

Quiz

•

9th - 12th Grade

19 questions

DCA review - Exponent Rules

Quiz

•

9th - 12th Grade

20 questions

Dilations

Quiz

•

9th - 12th Grade