Piecewise Functions homework Help at TutorEye

# Best Homework Help For Piecewise Functions

## 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

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 .

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.

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.

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.

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.

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 .

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

Answer: Domain Range Explanation: The lowest value of the function is , and it goes toward . Hence, the range would be .

Question 9: Find . And, write the domain of the function. Answer:  , and . And, Domain: Explanation: Analyze the domain of the function, and plug the value.

Question 10: Find . And, graph the function.  Answer:   Explanation: Analyze the domain of the function, and plug the value. 