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.

Tags

CCSS.HSF-IF.C.7B

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 is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals, such as (a, b) for open intervals and [a, b] for closed intervals.

Tags

CCSS.6.EE.B.8

Front

What does the notation (a, b) mean?

Back

The notation (a, b) represents an open interval, meaning it includes all numbers between a and b, but not a and b themselves.

Tags

CCSS.HSA.CED.A.3

Front

What does the notation [a, b] mean?

Back

The notation [a, b] represents a closed interval, meaning it includes all numbers between a and b, including a and b.

Tags

CCSS.HSA.CED.A.3

Front

How do you find the range of a piecewise function?

Back

To find the range, evaluate the outputs of each piece of the function over its domain and determine the set of all possible output values.

Front

What is the significance of the endpoints in piecewise functions?

Back

Endpoints determine whether the values at those points are included in the function (closed interval) or not (open interval).

Tags

CCSS.HSF-IF.C.7B

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, identify which piece of the function corresponds to that point's domain and use the appropriate formula.

Tags

CCSS.HSF.IF.A.2

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has exactly one output, while a relation can have multiple outputs for a single input.

Tags

CCSS.8.F.A.1

Front

What is a discontinuous piecewise function?

Back

A discontinuous piecewise function has at least one point where the function is not continuous, meaning there is a jump or break in the graph.

Tags

CCSS.HSF-IF.C.7B