Continuous Functions with Piecewise Functions

In summary, the individual has been working on exercise 5 and is unsure how to begin the problems. They initially thought to start with a graph, but now feel that may be incorrect. They are struggling with problems a and b, but were able to solve c and d which involve the application of continuity. They have also been reminded to post homework questions in the appropriate section with the proper format and to show their attempted solutions. The thread has been closed.
  • #1
KF33
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Member warned to post homework in a homework section
I have been working on this exercise 5 and kind of stuck how to start the problems. I would think to start with a graph, but I feel this is wrong. I am just stuck on a and b.
 

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  • #2
You can start with c and d. This is an application of the definition of continuity.
 
  • #3
Math_QED said:
You can start with c and d. This is an application of the definition of continuity.
Thanks I got c and d. The ones I am having trouble with are a and b.
 
  • #4
Please post homework problems in the Homework & Coursework sections, not here in the technical sections. Be sure to use the homework template and show what you have tried.
Thread closed.
 

1. What is a continuous function?

A continuous function is a mathematical function that has no abrupt changes or gaps in its graph. This means that the graph of a continuous function can be drawn without lifting your pen from the paper.

2. What is a piecewise function?

A piecewise function is a function that is defined by different rules or equations over different intervals of its domain. This means that the function may have different definitions for different parts of its domain.

3. What is the difference between a continuous function and a piecewise function?

The main difference between a continuous function and a piecewise function is that a continuous function is defined by a single rule or equation over its entire domain, while a piecewise function is defined by different rules or equations over different intervals of its domain. This means that a continuous function has a smooth and unbroken graph, while a piecewise function may have abrupt changes or gaps in its graph.

4. How do you determine if a piecewise function is continuous?

In order for a piecewise function to be continuous, it must have the same value at the points where the different pieces meet. This means that the limit of each piece of the function as it approaches the point of intersection must be equal to the value of the function at that point. Additionally, the function must also be continuous at all other points in its domain.

5. Can a piecewise function be differentiable?

Yes, a piecewise function can be differentiable at points where the different pieces of the function have the same slope. This means that the function must be continuous at these points and the derivative of each piece must be equal at the point of intersection. However, a piecewise function may not be differentiable at points where the different pieces have different slopes or the function is not continuous.

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