Piecewise Functions

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals of its domain.

Front

How do you determine the domain of a piecewise function?

Back

The domain of a piecewise function is the union of the domains of each piece, considering any restrictions from the individual pieces.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, identify which interval the point falls into and use the corresponding expression for that interval.

Front

What does it mean if a function is defined for all real numbers?

Back

If a function is defined for all real numbers, it means that there are no restrictions on the input values (x-values) for the function.

Front

What is the significance of the range being y ≤ 4?

Back

If the range is y ≤ 4, it means that the output values of the function can be any number less than or equal to 4.

Front

How do you calculate earnings based on a piecewise rate?

Back

To calculate earnings based on a piecewise rate, apply the appropriate rate to each segment of hours worked and sum the total earnings.

Front

What is the formula for calculating the total cost in a piecewise function?

Back

The total cost in a piecewise function is calculated by applying the cost formula for each segment of the input and summing the results.

Front

What is the importance of understanding the domain and range in piecewise functions?

Back

Understanding the domain and range helps in determining the valid input and output values for the function, which is crucial for graphing and solving problems.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval and ensure to indicate open or closed endpoints as necessary.