Piecewise Functions

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas over different intervals of its domain.

Front

How do you determine the domain of a piecewise function?

Back

To determine the domain, identify the intervals for which each piece of the function is defined and combine them.

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

What does it mean for a function to behave like a quadratic function?

Back

A function behaves like a quadratic function if it can be represented by a polynomial of degree 2, typically having a parabolic shape.

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 combine the resulting output values.

Front

What is the significance of domain restrictions in piecewise functions?

Back

Domain restrictions indicate the values of x for which the function is defined, helping to avoid undefined expressions.

Front

What is the difference between open and closed intervals?

Back

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

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval, ensuring to use open or closed dots as needed.

Front

What is an example of a piecewise function?

Back

An example is: f(x) = { x^2 for x < 0, 2x + 1 for x ≥ 0 }.

Front

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

Back

This notation signifies that the function f(x) is defined by multiple expressions based on the value of x.