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 does the domain of a function represent?

Back

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

Front

What does the range of a function represent?

Back

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

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 input value and then use the corresponding expression.

Front

What is the significance of the notation f(x)?

Back

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

Front

What does it mean if a function is defined as f(x) = {expression1, condition1; expression2, condition2}?

Back

It means that the function f takes on different expressions based on the conditions specified for the input x.

Front

What is the domain restriction of the function f(x) = {x^2, x < 0; 2x + 1, x ≥ 0}?

Back

The domain restriction is x < 0 for the first piece and x ≥ 0 for the second piece.

Front

How do you find the range of a piecewise function?

Back

To find the range, evaluate each piece of the function over its domain and determine the set of all possible output values.

Front

What is the difference between open and closed intervals in the context of domain and range?

Back

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

Front

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

Back

f(1) = 3.