Intro to Piecewise Functions

Front

What is a piecewise function?

Back

A piecewise function is comprised of multiple functions defined over different domains, such that together they pass the Vertical Line Test.

Front

Evaluate f(6) for the piecewise function given.

Back

f(6) = 3.

Front

How do you evaluate f(2) in a piecewise function?

Back

To evaluate f(2), identify the appropriate piece of the function for x=2 and calculate the output, which is 4.

Front

Evaluate f(1) for the piecewise function provided.

Back

f(1) = 4.

Front

What is the domain of the piecewise function?

Back

Front

What does the Vertical Line Test determine?

Back

The Vertical Line Test determines if a graph represents a function by checking if any vertical line intersects the graph at more than one point.

Front

What is the significance of restricted domains in piecewise functions?

Back

Restricted domains allow different rules or equations to apply to different intervals of the input, enabling more complex behaviors.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined domain and ensure continuity or discontinuity as specified.

Front

What is the output of a piecewise function at a boundary point?

Back

The output at a boundary point depends on whether the boundary is included (closed dot) or excluded (open dot) in the domain.

Front

How do you identify which piece of a piecewise function to use?

Back

Identify the input value and determine which interval it falls into based on the defined domains of the pieces.