Relations and Functions: Domain and Range

Which of the following options correctly represents the domain of a function?

Which of the following options correctly represents the range of a function?

What is the solution to the given inequality in interval notation?

What is the parent function of the given graph and how does its domain and range compare?

Which graph represents a function with a domain of [0, ∞) and a range of [0, ∞)?

Domain and Range Basics

The domain of a function comprises all possible x-values.
The range consists of all possible y-values.

Interval Notation

Example of an interval notation solution:
- [-4, ∞) indicates that the domain starts from -4 and extends to positive infinity, including -4.
- (-∞, 0) shows that the solution includes all values less than 0, excluding 0 itself.
- (0, 6) represents all values between 0 and 6, excluding both endpoints.

Parent Functions

The parent function is the simplest form of a function in a family of functions.
The domain and range of a parent function can be characterized by infinity, indicating it has no restrictions in either direction for both domain and range.
An analysis is needed to compare the domain and range of the parent function with that of a given graph to identify similarities and differences.

Identifying Functions

A function can be represented graphically, and certain characteristics, such as its domain and range, can be used to validate its classification.
Graph D represents a function with a domain of [0, ∞) and a range of [0, ∞), showing it starts from zero and includes all positive values.

Test your understanding of the domain and range in functions with this flashcard quiz. Each card focuses on key concepts such as x-values, y-values, and interval notation. Challenge yourself and reinforce your knowledge of these fundamental mathematical principles.