Domain and Range in Functions

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Questions and Answers

What does set builder notation primarily represent?

The conditions that define the elements of a set (correct)

The exact numerical values of a domain or range

The graphical representation of a function

The sequential order of data in a table

When determining the least x-value for domain representation, which aspect is most crucial?

The highest point on the graph along the y-axis

The value where the graph begins on the x-axis (correct)

The average of all x-values present in the data

The slope of the graph at its steepest point

In set builder notation, how is the inclusion of a value expressed?

By omitting the value entirely

By stating the value is less than or equal to another

Using parentheses around the value

Using square brackets around the value (correct)

Which of the following best describes the term 'range' in relation to a graph?

The interval of values along the y-axis (D) Signup and view all the answers

What is the primary purpose of scanning from bottom to top along the y-axis when determining the range?

To locate the minimum and maximum y-values in order (C) Signup and view all the answers

What does the domain of a function represent?

The set of all input values. (B) Signup and view all the answers

Which of the following describes a continuous graph?

Can be drawn without lifting the pencil. (A) Signup and view all the answers

How is the range of a function best described?

The set of all output values. (A) Signup and view all the answers

In which form is the domain of a discrete function typically expressed?

As a list of distinct points. (C) Signup and view all the answers

What would a graph with no restrictions on values likely indicate about its domain?

It represents all real numbers. (A) Signup and view all the answers

When determining the domain of a continuous graph, what axis should you scan?

X-axis. (C) Signup and view all the answers

Which statement about set builder notation is correct for the range of a function?

It can represent infinite points. (A) Signup and view all the answers

What does it mean if a set of ordered pairs does not represent a function?

At least one y-value is repeated for different x-values. (A) Signup and view all the answers

Which symbol is used in set builder notation to indicate a closed interval where the endpoint is included?

[ ] (A) Signup and view all the answers

How would you represent the domain of the function if it includes the endpoints in set builder notation?

{ x | a ≤ x ≤ b } (D) Signup and view all the answers

Given a graph where the least x-value is included and the greatest x-value is not included, which set builder notation is correct?

{ x | 2 ≤ x < 5 } (B) Signup and view all the answers

What is the purpose of using interval or set builder notation for domains and ranges?

To clearly convey included and excluded values (B) Signup and view all the answers

If a graph has an open circle at a x-value, how does it affect the set builder notation for the domain?

The x-value should use < in the notation (C) Signup and view all the answers

What symbol represents an open interval in set builder notation?

( ) (B) Signup and view all the answers

Which of the following correctly represents a situation where the least y-value is not included and the greatest y-value is included?

{ y | 1 < y ≤ 10 } (C) Signup and view all the answers

When using interval notation for a domain that extends indefinitely towards negative infinity and includes -3, what would be its representation?

(-∞, -3] (D) Signup and view all the answers

Study Notes

Domain and Range Notes

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

Writing Domain and Range

Discrete (Finite) Graphs: Domain and range consist of separate, distinct values. These are often represented by lists of numbers or points, like ordered pairs, tables, mappings, or scatter plots.
Continuous Graphs: The domain and range can be infinite and are often expressed as intervals or set-builder notation. A continuous graph is one that you can draw without lifting your pencil. These graphs can include lines, curves, or combinations of those.

Set Builder Notation

Use symbols like "x ∈" (x is an element of), "such that" or "≥" (greater than or equal to), "<" (less than), ">=" (greater than or equal to), and "<=" (less than or equal to) to describe the conditions for the domain and/or range.

Interval Notation

Uses parentheses and brackets to show whether or not endpoints are included in the interval. Parentheses exclude the endpoint (e.g., (2, 5) means the values between 2 and 5 but not including 2 or 5 themselves). Brackets include the endpoint (e.g., [2, 5] means all the values between 2 and 5, including 2 and 5).

Graphing to Find Domain and Range

Continuous graphs: Use the x-axis to determine the domain (scanning from left to right). Use the y-axis to determine the range (scanning from bottom to top).
Discrete graphs: Identify all the separate points on the graph. The x-coordinates represent the domain, and the y-coordinates represent the range.

Examples (from document)

Examples of discrete and continuous graphs, tables, mappings and ordered pairs show different ways to represent domains and ranges.

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Description

This quiz covers the concepts of domain and range in mathematical functions. You'll learn how to identify these using discrete and continuous graphs, along with the application of set-builder notation. Test your understanding and improve your skills in analyzing functions.