Algebra 2. Graphing 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 graph a piecewise function?

Back

To graph a piecewise function, identify the intervals for each piece, graph each piece according to its formula, and ensure to use open or closed circles to indicate whether endpoints are included.

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 at the points where the pieces meet.

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, considering all 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 (y-values) that the function can produce.

Front

How do you determine the value of a piecewise function at a specific point?

Back

To determine the value of a piecewise function at a specific point, identify which interval the point falls into and use the corresponding expression to calculate the output.

Front

What is an example of a piecewise function?

Back

An example of a piecewise function is: f(x) = { x^2 for x < 0; 2x + 1 for x >= 0 }.

Front

What is the significance of open and closed circles in graphing piecewise functions?

Back

Open circles indicate that a point is not included in the function (not part of the graph), while closed circles indicate that the point is included.

Front

How can you identify the intervals of a piecewise function from its graph?

Back

You can identify the intervals of a piecewise function from its graph by observing where the function changes its formula or expression.

Front

What is the slope of a linear piece in a piecewise function?

Back

The slope of a linear piece in a piecewise function is the ratio of the change in y to the change in x (rise over run) for that segment.