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 the input variable.

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, determine which interval the input value falls into and then use the corresponding expression to find the output.

Front

What does the term 'domain' refer to in piecewise functions?

Back

The domain of a piecewise function refers to the set of all possible input values (x-values) for which the function is defined.

Front

What does the term 'range' refer to in piecewise functions?

Back

The range of a piecewise function refers to the set of all possible output values (y-values) that the function can produce.

Front

How many pieces are in the function f(x) = { x^2 for x < 0; 2x + 1 for x >= 0 }?

Back

There are 2 pieces in this function.

Front

What is the output of f(4) for the function f(x) = { -3 for x < 0; x + 1 for x >= 0 }?

Back

The output is 5.

Front

What is the output of f(-2) for the function f(x) = { -3 for x < 0; x + 1 for x >= 0 }?

Back

The output is -3.

Front

What is the significance of the 'breakpoints' in piecewise functions?

Back

Breakpoints are the values of x where the function changes from one piece to another, indicating where the definition of the function switches.

Front

If f(x) = { 2x for x < 1; 3 for x = 1; x^2 for x > 1 }, what is f(1)?

Back

f(1) = 3.

Front

What is the graphical representation of a piecewise function?

Back

A piecewise function is represented graphically by connecting different line segments or curves, each corresponding to a specific interval of the domain.