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 parts of its domain.

Front

How do you determine the domain of a piecewise function?

Back

The domain of a piecewise function is determined by the intervals for which each piece of the function is defined.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

Front

What is the significance of the 'breakpoints' in a piecewise function?

Back

Breakpoints are the values of x at which the function changes from one piece to another.

Front

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

Back

To evaluate a piecewise function at a specific point, identify which piece of the function applies to that point and use the corresponding formula.

Front

What is the range of a piecewise function?

Back

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

Front

What is the difference between an open interval and a closed interval?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval, ensuring to use open or closed dots as appropriate.

Front

What is the formula for a linear piece in a piecewise function?

Back

The formula for a linear piece is typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the value of f(x) for x in a specific interval?

Back

To find f(x) for x in a specific interval, use the formula that corresponds to that interval.