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 determine the domain of a piecewise function?

Back

The domain of a piecewise function is the union of the domains of each piece, considering the intervals where each piece is defined.

Front

What does it mean for a function to behave like a linear function?

Back

Front

What does it mean for a function to behave like a quadratic function?

Back

Front

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

Back

Breakpoints are the values in the domain where the function changes from one expression to another, affecting the function's behavior.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function over its specified interval and ensure to indicate open or closed circles at breakpoints.

Front

What is the notation used for piecewise functions?

Back

Piecewise functions are often written using braces, for example: @@f(x) = \begin{cases} x^2 & \text{if } x < 0 \\ 2x + 1 & \text{if } x \geq 0 \end{cases}@@.

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, based on its defined pieces.

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 output.

Front

What is an example of a piecewise function?

Back

An example of a piecewise function is: @@f(x) = \begin{cases} x + 2 & \text{if } x < 1 \\ 3 & \text{if } x = 1 \\ x^2 & \text{if } x > 1 \end{cases}@@.