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 the domain of a function?

Back

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

Front

How do you find the value of a piecewise function at a specific point?

Back

To find the value of a piecewise function at a specific point, determine which piece of the function applies to that input value and then evaluate the function using that expression.

Front

What does the notation f(x) = { ... } represent?

Back

This notation represents a piecewise function, where different expressions are used for different intervals of x.

Front

What is the range of a function?

Back

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

Front

If f(x) = { x if x < 4; -x + 1 if x ≥ 4, what is f(3)?

Back

f(3) = 3, since 3 < 4.

Front

If f(x) = { -x + 1 if x < 4; x if x ≥ 4, what is f(4)?

Back

f(4) = 4, since 4 ≥ 4.

Front

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

Back

Endpoints determine whether the function includes or excludes certain values in its domain, affecting continuity and limits.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval, ensuring to use open or closed circles at endpoints as needed.

Front

What is an example of a piecewise function?

Back

An example is f(x) = { x^2 if x < 0; 2x + 1 if x ≥ 0.