Piecewise

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 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 use the corresponding expression to find the function's value.

Front

What is interval notation?

Back

Interval notation is a way of representing a range of values using parentheses and brackets to indicate whether endpoints are included or excluded.

Front

What does the notation (-9, -4] represent?

Back

The notation (-9, -4] represents all real numbers greater than -9 and less than or equal to -4.

Front

How do you express the domain of a piecewise function?

Back

The domain of a piecewise function is expressed as the union of the intervals for which each piece of the function is defined.

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include its endpoints, while a closed interval [a, b] includes its endpoints.

Front

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

Back

To find f(x) for a piecewise function, identify the correct piece of the function based on the value of x and substitute x into that piece.

Front

What is the significance of the notation DNE in piecewise functions?

Back

DNE stands for 'Does Not Exist' and is used to indicate that a function value is undefined for a particular input.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval, using open or closed dots to indicate whether endpoints are included.

Front

What is the output of f(-2) if f(x) = { 4 if x < -2; 8 if x >= -2 }?

Back

The output of f(-2) is 8, since -2 falls into the second piece of the function.