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 determine the domain of a piecewise function?

Back

The domain of a piecewise function is the union of the domains of each piece, considering any restrictions.

Front

What does the notation f(x) = { expression1 for x in interval1, expression2 for x in interval2 } represent?

Back

This notation represents a piecewise function where different expressions are used for different intervals of x.

Front

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

Back

Intervals determine where each piece of the function applies, affecting the function's output based on the input value.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece on its respective interval, ensuring to use open or closed dots based on the inequality.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values, which can be found by evaluating each piece.

Front

What does it mean if a piecewise function has a discontinuity?

Back

A discontinuity in a piecewise function means there is a jump or break in the graph, indicating that the function is not continuous at that point.

Front

How do you find the value of x for a given y in a piecewise function?

Back

To find x for a given y, set the piecewise function equal to y and solve for x within the appropriate interval.

Front

What is the difference between an open interval and a closed interval?

Back

An open interval does not include its endpoints (e.g., (a, b)), while a closed interval includes its endpoints (e.g., [a, b]).

Front

How do you identify the number of pieces in a piecewise function?

Back

Count the number of distinct expressions or formulas defined for different intervals in the function.