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 parts of its domain.

Front

What is a step function?

Back

A step function is a type of piecewise function that has a graph resembling a series of steps, where the function value remains constant within certain intervals.

Front

What does the notation f(x) = { x if x < 4; -x+1 if x ≥ 4 mean?

Back

This notation defines a piecewise function where for values of x less than 4, f(x) equals x, and for values of x greater than or equal to 4, f(x) equals -x + 1.

Front

How do you determine the domain of a piecewise function?

Back

To determine the domain of a piecewise function, identify the intervals for which each piece of the function is defined and combine them.

Front

What is the domain restriction for the function f(x) = { -x+1 if x < 4; x if x ≥ 4?

Back

The domain restriction is all real numbers, as both pieces are defined for all x.

Front

What is the range of the function f(x) = { -x+1 if x < 4; x if x ≥ 4?

Back

The range is all real numbers, as the function can take any value depending on the input.

Front

What is the significance of the point where the pieces of a piecewise function meet?

Back

The point where the pieces meet is called a breakpoint, and it is important for determining continuity and the overall behavior of the function.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval and ensure to indicate open or closed circles at the endpoints.

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 breakpoints.

Front

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

Back

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