Linear Piecewise Functions

Front

What is a Linear Piecewise Function?

Back

A function that is defined by different expressions based on the input value (x).

Front

What is the general form of a piecewise function?

Back

f(x) = { expression1 for x < a, expression2 for x >= a }.

Front

What is a Step Function?

Back

A type of piecewise function that has a graph resembling a staircase, with constant values over intervals.

Front

What does the DOMAIN of a function represent?

Back

The set of all possible input values (x) for which the function is defined.

Front

What is the range of a function?

Back

The set of all possible output values (f(x)) that the function can produce.

Front

How do you evaluate f(x) for piecewise functions?

Back

Determine which piece of the function applies based on the value of x, then substitute x into that piece.

Front

What is the value of f(-2) for the function f(x) = 4 - x for x < 2?

Back

f(-2) = 4 - (-2) = 6.

Front

What is the value of f(-1) for the function f(x) = 2x - 6 for x >= 2?

Back

DNE (Does Not Exist) because -1 is not in the domain of that piece.

Front

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

Back

It is called a 'breakpoint' and can indicate a change in the function's behavior.

Front

How do you graph a piecewise function?

Back

Plot each piece of the function separately, ensuring to use open or closed dots based on the inequality.