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 for the following piecewise function.

Answer:

Explanation: Analyze the domain of each function

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

Answer:

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

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Question 3: Graph the following piecewise function.

Answer:

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.

Answer:

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.

Answer: Domain:

Range:

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.

Answer: Domain:

Range:

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

Answer: The function is continuous at

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 .

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