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, determine which interval the input value falls into and then use the corresponding 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 possible input values (x-values) for which the function is defined.

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

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

Back

f(-2) = (-2)^2 = 4.

Front

If g(x) = { -x - 3 for x < 0; x + 10 for x ≥ 0, what is g(7)?

Back

g(7) = 7 + 10 = 17.

Front

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

Back

f(0) = 2(0) + 4 = 4.

Front

What are domain restrictions in piecewise functions?

Back

Domain restrictions specify the intervals for which each piece of the function is valid.

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 inclusivity of the endpoints.

Front

What is the range of a piecewise function?

Back

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