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.

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 the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x-values) for which the function is defined, often specified by the intervals of each piece.

Front

What does it mean for a piecewise function to be continuous?

Back

A piecewise function is continuous if there are no breaks, jumps, or holes in the graph, meaning the function's value approaches the same limit from both sides at the boundaries of the pieces.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval, ensuring to use open or closed dots to indicate whether endpoints are included.

Front

What is the significance of the domain restrictions in piecewise functions?

Back

Domain restrictions in piecewise functions indicate the specific intervals where each piece of the function is applicable, ensuring the function is defined only where intended.

Front

Evaluate f(0) for the piecewise function defined as: f(x) = { 0 if x < 0, 1 if x = 0, 3 if x > 0 }

Back

f(0) = 1.

Front

Evaluate f(4) for the piecewise function defined as: f(x) = { -5 if x < 0, 0 if x = 0, 3 if x > 0 }

Back

f(4) = 3.

Front

What is the value of f(x) when x = 0 for the function f(x) = { 0 if x < 0, 1 if x = 0, 2 if x > 0 }?

Back

f(0) = 1.

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, determined by the outputs of each piece.