Chapter 14: Q. 27 (page 889)

In Problems 13–32, use the accompanying graph of y = f(x).
Is f continuous at -6?

Short Answer

Expert verified

The answer is no. The function is not continuous at -6.

Step by step solution

Step. 1 How to check continuity?

For a function to be continuous its LHL = RHL = f(c) at the point $x = c$ .

Step. 2 Calculating LHL, RHL and f(c).

As we can see that $x = - 6$ doesn't exist even in the domain of f(x).

So, f(-6) doesn't exist. Therefore, we don't need to calculate LHL and RHL from here itself we can conclude that f(x) is not continuous at $x = - 6$ .

And from the graph itself we can clearly see that we have to pick our pencil up the paper when we move through $x = - 6$ which is also a method to check whether the function is continuous or not.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 13–32, use the accompanying graph of y = f(x).
Is f continuous at -6?

Short Answer

Step by step solution

Step. 1 How to check continuity?

Step. 2 Calculating LHL, RHL and f(c).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Applied Mathematics

Calculus

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

In Problems 13–32, use the accompanying graph of y = f(x).Is f continuous at -6?

Short Answer

Step by step solution

Step. 1 How to check continuity?

Step. 2 Calculating LHL, RHL and f(c).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Applied Mathematics

Calculus

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

In Problems 13–32, use the accompanying graph of y = f(x).
Is f continuous at -6?