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Piecewise Functions:

A function where more than one piece of function is used to define the output is called the piecewise function. Each piece of the function is defined on a certain interval. And, the domain of the piecewise function would be the union of domains of all the pieces of function.

 

Piecewise Functions Sample Questions:

Question 1: Find the value of Find the value for the following piecewise function.


piecewise function


Answer: solution

Explanation: Analyze the domain of each function

 

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Question 2: Find the value of the value for the following piecewise function.


following piecewise function.


Answer: solution 2

Explanation: Because value, to find the value of find the value of, we need to plug we need to plug in the function function.

 

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Question 3: Graph the following piecewise function.


Graph the following piecewise function.



Answer: Graph

Explanation: We will use the domain of each piece of the function, and plot the graph accordingly.

 

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Question 4: A company charges its customer in USD based on the following function for renting a car. Find the cost for first two km. And, for the 10 km of journey.


A company charges its customer in USD based on the following function


Answer: solution 3

Explanation: To find the cost of renting a car for a specific distance, we need to analyze the domain of each piece of the function.

 

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Question 5: Write the range and domain of the piecewise function.


range and domain of the piecewise function


Answer: Domainsolution 4

Rangerange

Explanation: The domain is a set of all real values for which function is defined and has a real value.

 

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Question 6: Write the range and domain of the piecewise function.


range and domain of the piecewise function.


Answer: Domaindomain

Rangerange 2

Explanation: The given piecewise function is defined over or . Let us write the interval notation and take union.

 

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Question 7: Check if the following piecewise function is continuous at


piecewise function is continuous at


question 7


Answer: The function is continuous at solution

Explanation: To check the continuity of the function at , we need to analyze the left-hand and right-hand side limit and value of the function at the point The function is continuous at .

 

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Question 8: Plot the function Plot the function, and write its domain and range.



Answer: graph 2

DomainDomain 8

Rangerange 3

Explanation: The lowest value of the function is Find , and it goes toward write the domain of the function. Hence, the range would be Analyze the domain of the function.

 

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Question 9: Find Find 2. And, write the domain of the function.

write the domain of the function


Answer: solution 9value of f(8), and Domain 9. And, Domain: range 9

Explanation: Analyze the domain of the function, and plug the value.

 

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Question 10: Find Find 5. And, graph the function.


graph the function


Graph 4


Answer: solution 10.1solution 10.2solution 10.3

Explanation: Analyze the domain of the function, and plug the value.

 

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