Evaluating 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.

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

Back

To evaluate a piecewise function at a specific point, determine which interval the point falls into and then use the corresponding expression to find the function's value.

Front

What is the significance of the domain in a piecewise function?

Back

The domain of a piecewise function indicates the set of input values for which the function is defined, which may vary across different pieces.

Front

How do you find the value of f(x) for x = 1 in a piecewise function?

Back

Identify the interval that includes x = 1 and use the corresponding expression to calculate f(1).

Front

What does it mean if a piecewise function is continuous at a point?

Back

A piecewise function is continuous at a point if the limit from the left and the limit from the right at that point are equal to the function's value at that point.

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What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (f(x)) that the function can produce based on its defined pieces.

Front

How do you determine the cost for a group of people using a piecewise function?

Back

To determine the cost for a group of people, identify the relevant piece of the function that applies to the size of the group and evaluate it accordingly.

Front

What is the formula for finding the cost for a group of 20 people if the cost is defined piecewise?

Back

The formula will depend on the specific piece of the function that applies to groups of 20; evaluate that piece to find the total cost.

Front

What is the difference between open and closed intervals in the context of piecewise functions?

Back

Open intervals do not include their endpoints, while closed intervals do include their endpoints, affecting the domain of the function.

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How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval and ensure to indicate whether endpoints are included or excluded.