Piecewise Practice

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, plot each piece of the function on its respective interval, ensuring to use open or closed dots based on whether the endpoints are included.

Front

What does the notation f(x) = { expression1, expression2 } mean?

Back

This notation indicates that the function f(x) has different expressions for different values of x, typically defined by conditions.

Front

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

Back

The domain specifies the intervals over which each piece of the function is valid, which is crucial for accurate graphing and evaluation.

Front

How do you determine the equation of a piecewise function from a graph?

Back

Identify the different segments of the graph, note their slopes and intercepts, and write the corresponding equations for each segment based on their defined intervals.

Front

What is an inequality in the context of piecewise functions?

Back

An inequality describes the range of x-values for which a particular piece of the function is applicable, often represented in interval notation.

Front

What does it mean if a piecewise function has a closed dot at an endpoint?

Back

A closed dot indicates that the endpoint is included in the function's domain, meaning the value at that point is part of the function.

Front

What does it mean if a piecewise function has an open dot at an endpoint?

Back

An open dot indicates that the endpoint is not included in the function's domain, meaning the value at that point is not part of the function.

Front

How can you express the solution to a piecewise function graphically?

Back

The solution can be expressed by shading the regions of the graph that correspond to the valid intervals of x for each piece of the function.

Front

What is the relationship between piecewise functions and inequalities?

Back

Piecewise functions often involve inequalities to define the intervals for which each piece of the function is valid.