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

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

Back

To evaluate a piecewise function at a specific point, determine which piece of the function applies to that point based on its domain.

Front

What does the notation f(x) mean in piecewise functions?

Back

f(x) represents the output of the function for a given input x, which may depend on the piece of the function that corresponds to x.

Front

If f(x) = { x^2 for x < 0; 2x + 1 for x >= 0, what is f(-3)?

Back

f(-3) = (-3)^2 = 9.

Front

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

Back

f(1) = 2.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x) for which the function is defined, which may vary across different pieces.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval and ensure to use open or closed circles to indicate whether endpoints are included.

Front

What is the range of a piecewise function?

Back

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

Front

If f(x) = { 2 for x < 0; x + 3 for 0 <= x < 5; 10 for x >= 5, what is f(4)?

Back

f(4) = 4 + 3 = 7.

Front

What is the significance of 'pieces' in a piecewise function?

Back

The 'pieces' refer to the different segments of the function, each defined by its own rule or formula for specific intervals of the domain.