Domain and Range Class Notes

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Questions and Answers

How is the domain represented in set builder notation?

{x | a < x < b}

{x | x > a and x < b} (correct)

{x | x ≤ a or x ≥ b}

{x | x = a or x = b}

What does scanning from bottom to top along the y-axis help identify?

The least y-value only

The range of y-values (correct)

The greatest x-value only

The domain of the x-values

What type of questions are asked to determine if a graph is a function?

Does each x-value correspond to exactly one y-value? (correct)

Is the least y-value included?

Is the greatest x-value included?

Is the domain represented in correct notation?

Which of the following statements is false regarding domain and range?

The greatest y-value is always included. Signup and view all the answers

Which notation is commonly used to represent the range of a function?

Set builder notation Signup and view all the answers

What defines the domain of a function?

The set of all input values or x-values Signup and view all the answers

How is the range of a function described?

It represents all possible output values. Signup and view all the answers

In which scenario would the domain be written as 'all real numbers'?

When a continuous graph has no restrictions. Signup and view all the answers

Which representation is correct for a finite domain?

List of separate values Signup and view all the answers

When scanning the x-axis for a continuous graph, which action is performed?

Scan from left to right for connected points. Signup and view all the answers

What must be true for a set of ordered pairs to represent a function?

Each x-value must map to one and only one y-value. Signup and view all the answers

How can the range of a continuous function be represented?

As a simple inequality Signup and view all the answers

What is the independent variable in a function?

The input value or x-value Signup and view all the answers

What symbol in set builder notation indicates that an endpoint is included?

[ Signup and view all the answers

Which of the following represents an OPEN interval in set builder notation?

{x | x > 2} Signup and view all the answers

In set builder notation, how would you represent a domain with a lowest point of 3 included and no upper limit?

{x | 3 ≤ x < ∞} Signup and view all the answers

Which notation would be appropriate for a range that includes all values greater than or equal to -1?

{y | y ≥ -1} Signup and view all the answers

If a graph has a least x-value of 4 (included) and a greatest x-value of 10 (not included), what is the set builder notation for the domain?

{x | 4 ≤ x < 10} Signup and view all the answers

What is the representation in set builder notation for a range that includes all real numbers less than 5?

{y | y < 5} Signup and view all the answers

If a graph indicates a least y-value of -2 (not included) and a greatest y-value of 3 (included), how should the range be expressed?

{y | -2 < y ≤ 3} Signup and view all the answers

For a function with endpoints at 1 and 4, both included, how is the domain represented in set builder notation?

{x | 1 ≤ x ≤ 4} Signup and view all the answers

Study Notes

Domain and Range Notes

Domain: The set of all input values (x-values) for a function or relation. These values correspond to the points on the graph's x-axis.
Range: The set of all output values (y-values) for a function or relation. These values correspond to the points on the graph's y-axis.

Writing Domain and Range

Discrete Data: For graphs with separate, distinct points (e.g., a list of ordered pairs, a table, a mapping, or scatter plot): Write the x-values and y-values separately.
Continuous Data: For graphs with connected points that can be drawn without lifting a pen (e.g., lines, curves, continuous graphs): Use inequalities or interval notation to represent the domain and range. The endpoints determine whether to use [ ]. (closed circle, included) or ( ). (open circle, not included).
Continuous graphs: Scan the x-axis from the lowest to the highest point to find the domain. Scan the y-axis from the lowest to highest point to find the range. Always write from least to greatest.

Set Builder Notation

Set builder notation: A way to describe a set of numbers.
Example: { x | x ≥ 3 } means "the set of all x such that x is greater than or equal to 3."
Use x for domain and y for range in set-builder notation.
Use ≤ or ≥ when the endpoint is included.
Use < or > when the endpoint is not included.
For infinite ranges use −∞ (negative infinity) and ∞ (positive infinity) in interval notation.

Examples of Discrete Data

Tables: Data presented in rows and columns (miles and hours, input and output).
Mappings: Visual representations of input-output pairs, often using arrows to show relationships
Ordered Pairs: A set of pairs of numbers like {(9,2), (3,4)...}

Examples of Continuous Data

Graphs: Visual representations of functions or relations.
Lines/Curves: Straight lines, curved lines.

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Description

This quiz covers the concepts of domain and range in functions, including how to identify and write them for both discrete and continuous data. It includes instructions for using graph points and interval notation to accurately represent these values. Perfect for students studying algebra and functions.