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?

Back

To evaluate a piecewise function, determine which piece of the function applies to the given input value and then use that expression to find the output.

Front

What is the domain of a piecewise function?

Back

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

Front

What does 'DNE' stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a function value is not defined for a particular input.

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, ensuring to use open or closed dots as appropriate.

Front

What is the significance of the domain restriction in piecewise functions?

Back

Domain restrictions indicate the specific input values for which each piece of the function is valid, affecting the overall behavior of the function.

Front

What is the value of f(0) if f(x) = { 2x + 1 for x < 0; 4 for x ≥ 0 }?

Back

f(0) = 4.

Front

If f(x) = { x^2 for x < 0; 2x for x ≥ 0 }, what is f(-2)?

Back

f(-2) = 4.

Front

What is the output of f(1) if f(x) = { x + 3 for x < 2; x^2 for x ≥ 2 }?

Back

f(1) = 4.

Front

What is the difference between open and closed intervals in piecewise functions?

Back

Open intervals do not include endpoints (e.g., (a, b)), while closed intervals do include endpoints (e.g., [a, b]).