what is the domain and range ### Graph Analysis and Function Determination#### Does the graphed relation define a function?- Options: - Yes - No (selected)The graphed relation does not define a function because it fails the Vertical Line Test. The Vertical Line Test states that for a graph to represent a function, no vertical line should intersect the graph at more than one point. In this graph, vertical lines intersect the curve at multiple points.#### What is the domain of the graphed relation?✔ (Type your answer in interval notation.)### Graph DescriptionThe graph plotted is located on a Cartesian coordinate system with $ x $-axis ranging from -10 to 10 and $ y $-axis ranging from -10 to 10. The graph displays a curve that moves upward from the right and veers towards the left before looping back to the right. This shape clearly shows multiple $ y $-values for certain $ x $-values, which means it does not pass the Vertical Line Test, confirming the relation is not a function.### Domain and Range Explanation**Domain:** The domain of a relation is the set of all possible $ x $-values. Since the graph extends horizontally from around $ x = -10 $ to $ x = 10 $, the domain can generally be represented in interval notation. However, the exact boundaries should be observed and one should input the correct interval according to the plotted curve.**Range:** The range of a relation is the set of all possible $ y $-values. The graph appears to vertically span from approximately $ y = -8 $ to $ y = 8 $ (though not explicitly asked for in this question, knowing the range is necessary for a full understanding).Students should enter their determined domain in the provided box using interval notation. For example, if the correct domain extends from $ x = -10 $ to $ x = 10 $, the appropriate input would be $(-10, 10)$.

Decide whether the relation defined by the graph to the right defines a function, and give the domain and range. Ay 10- Does the graphed relation define a function? 6- Yes 4- V No -10 -6 -4 -2 -2- 10 What is the domain of the graphed relation? -4- -6- (Type your answer in interval notation.) 10

Decide whether the relation defined by the graph to the right defines a function, and give the domain and range. Ay 10- Does the graphed relation define a function? 6- Yes 4- V No -10 -6 -4 -2 -2- 10 What is the domain of the graphed relation? -4- -6- (Type your answer in interval notation.) 10

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

what is the domain and range

### Graph Analysis and Function Determination

#### Does the graphed relation define a function?
- Options:
- Yes
- No (selected)

The graphed relation does not define a function because it fails the Vertical Line Test. The Vertical Line Test states that for a graph to represent a function, no vertical line should intersect the graph at more than one point. In this graph, vertical lines intersect the curve at multiple points.

#### What is the domain of the graphed relation?
✔ (Type your answer in interval notation.)

### Graph Description

The graph plotted is located on a Cartesian coordinate system with $ x $-axis ranging from -10 to 10 and $ y $-axis ranging from -10 to 10. The graph displays a curve that moves upward from the right and veers towards the left before looping back to the right. This shape clearly shows multiple $ y $-values for certain $ x $-values, which means it does not pass the Vertical Line Test, confirming the relation is not a function.

### Domain and Range Explanation

**Domain:** The domain of a relation is the set of all possible $ x $-values. Since the graph extends horizontally from around $ x = -10 $ to $ x = 10 $, the domain can generally be represented in interval notation. However, the exact boundaries should be observed and one should input the correct interval according to the plotted curve.

**Range:** The range of a relation is the set of all possible $ y $-values. The graph appears to vertically span from approximately $ y = -8 $ to $ y = 8 $ (though not explicitly asked for in this question, knowing the range is necessary for a full understanding).

Students should enter their determined domain in the provided box using interval notation. For example, if the correct domain extends from $ x = -10 $ to $ x = 10 $, the appropriate input would be $(-10, 10)$.

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