**Title: Understanding Functions in Graphical Form****Introduction:**In this lesson, we will decide whether the relation defined by a graph defines a function and determine its domain and range. **Does the Graphed Relation Define a Function?**- **No**- **Yes** (✔️)**Explanation:**To determine if the graphed relation is a function, we can perform the Vertical Line Test. If any vertical line intersects the graph at more than one point, the relation is not a function. If every vertical line intersects the graph at most once, the relation is a function.In the provided graph, every vertical line intersects the graph at most once, hence the relation defines a function. **Graph Explanation:**The graphed relation depicted is a blue curve on a coordinate plane with:- The x-axis ranging from -6 to 6.- The y-axis ranging from -10 to 10.- The graph shows a continuous curve that starts from the lower left quadrant, moves upwards crossing the y-axis once, forms a peak around (0, 6), descends to form a trough around (-4, 0), and ascends up to the right quadrant.**What is the Domain of the Graphed Relation?**To find the domain, look at the extent of the x-values covered by the graph. The graph extends indefinitely along the x-axis in both directions.- **Domain:** (Type your answer in interval notation.)**Solution:**The domain is all real numbers because the graph continues indefinitely in both the positive and negative directions along the x-axis.- **Domain:** (-∞, ∞)**Conclusion:**To summarize, we determined that the given graph defines a function by using the Vertical Line Test. We also identified the domain of the function, which includes all real numbers.**Interactive Exercise:**- Apply the Vertical Line Test to the graph.- Determine the range of the graphed function.**Note:**Understanding the domain and range of functions is crucial in the study of mathematics, as it helps in identifying the possible values that a function can take and the possible input numbers.

Answered: Image /qna-images/answer/fb483e36-08f2-47d7-b82b-fa71822017b7.jpg

Decide whether the relation defined by the graph to the right defines a function, and give the domain and range. Ay 10어 Does the graphed relation define a function? 6- O No 4- V Yes 2- What is the domain of the graphed relation? -2- -4- -6- (Type your answer in interval notation.) -8- -10-

Decide whether the relation defined by the graph to the right defines a function, and give the domain and range. Ay 10어 Does the graphed relation define a function? 6- O No 4- V Yes 2- What is the domain of the graphed relation? -2- -4- -6- (Type your answer in interval notation.) -8- -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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Question

**Title: Understanding Functions in Graphical Form**

**Introduction:**

In this lesson, we will decide whether the relation defined by a graph defines a function and determine its domain and range.

**Does the Graphed Relation Define a Function?**

- **No**
- **Yes** (✔️)

**Explanation:**
To determine if the graphed relation is a function, we can perform the Vertical Line Test. If any vertical line intersects the graph at more than one point, the relation is not a function. If every vertical line intersects the graph at most once, the relation is a function.

In the provided graph, every vertical line intersects the graph at most once, hence the relation defines a function.

**Graph Explanation:**

The graphed relation depicted is a blue curve on a coordinate plane with:

- The x-axis ranging from -6 to 6.
- The y-axis ranging from -10 to 10.
- The graph shows a continuous curve that starts from the lower left quadrant, moves upwards crossing the y-axis once, forms a peak around (0, 6), descends to form a trough around (-4, 0), and ascends up to the right quadrant.

**What is the Domain of the Graphed Relation?**

To find the domain, look at the extent of the x-values covered by the graph. The graph extends indefinitely along the x-axis in both directions.

- **Domain:** (Type your answer in interval notation.)

**Solution:**
The domain is all real numbers because the graph continues indefinitely in both the positive and negative directions along the x-axis.

- **Domain:** (-∞, ∞)

**Conclusion:**

To summarize, we determined that the given graph defines a function by using the Vertical Line Test. We also identified the domain of the function, which includes all real numbers.

**Interactive Exercise:**

- Apply the Vertical Line Test to the graph.
- Determine the range of the graphed function.

**Note:**
Understanding the domain and range of functions is crucial in the study of mathematics, as it helps in identifying the possible values that a function can take and the possible input numbers.

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