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

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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

What is a step function?

Back

A step function is a type of piecewise function that has a graph resembling a series of steps, where the function value remains constant within certain intervals.

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, determine which piece of the function applies to the given input value and then use that expression to find the output.

Front

What does f(-3) represent in a function?

Back

f(-3) represents the output of the function when the input is -3.

Front

If f(x) = { x + 2 for x < 0; x^2 for x ≥ 0 }, what is f(2)?

Back

f(2) = 2^2 = 4.

Front

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

Back

Breakpoints are the values at which the function changes from one expression to another, often corresponding to the boundaries of the intervals.

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 circles at breakpoints.

Front

What is the difference between continuous and discontinuous piecewise functions?

Back

Continuous piecewise functions have no breaks in their graphs, while discontinuous piecewise functions have jumps or gaps.