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 its domain.

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, identify the interval that contains the input value and use the corresponding expression to find the output.

Front

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

Back

f(x) represents the output of the function for a given input x.

Front

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

Back

f(-3) = -3 + 2 = -1.

Front

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

Back

f(1) = 3.

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.

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

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 use open or closed dots based on the inclusion of endpoints.

Front

What is the significance of the endpoints in a piecewise function?

Back

Endpoints determine whether the function includes or excludes certain values, affecting the continuity of the graph.

Front

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

Back

This function has 3 pieces.