Piecewise Functions

Front

What is a piecewise function?

Back

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

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, identify the interval that the input value falls into and use the corresponding expression to find the output.

Front

What is the domain of a piecewise function?

Back

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

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values, which can also vary depending on the piece being evaluated.

Front

If f(x) = { x^2 for x < 0; 2x for x >= 0, what is f(-3)?

Back

f(-3) = 9, since -3 falls in the interval x < 0.

Front

If f(x) = { 3x + 1 for x < 1; x^2 for x >= 1, what is f(2)?

Back

f(2) = 4, since 2 falls in the interval x >= 1.

Front

What is the importance of the 'break' in a piecewise function?

Back

The 'break' indicates where the function changes its rule or formula, which is crucial for understanding its behavior.

Front

How can piecewise functions be graphed?

Back

Piecewise functions can be graphed by plotting each piece separately over its defined interval and ensuring continuity where applicable.

Front

What is a common application of piecewise functions?

Back

Piecewise functions are commonly used in real-world scenarios, such as tax brackets, shipping costs, and rental rates.

Front

If a piecewise function has a discontinuity, what does that mean?

Back

A discontinuity in a piecewise function means there is a 'jump' or 'break' in the graph where the function is not continuous.