Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![### Understanding the Domain of a Function from a Graph
Below is a graph of a function. This graph helps us visualize the behavior and scope of the function within a specific range.
#### Graph Description:
- The graph has a set of axes marked from -6 to 6 on both the x-axis and y-axis.
- The function depicted is a part of an upward-facing parabola.
- The left side of the parabola starts just below the y-axis at the point (-2, -1), denoted with an open circle, indicating that this point is not included in the function.
- The right side of the parabola ends at the point (1, 1), marked with a closed circle, indicating that this point is included in the function.
- The lowest point of the curve, or vertex, appears to be at around (-0.5, -2).
#### Task:
**Write the domain of the function using interval notation.**
The domain of a function includes all possible input values (x-values) that the function can accept. Based on the given graph, the function starts at \( x = -2 \) and ends at \( x = 1 \).
- Since the graph has an open circle at \( x = -2 \), the value -2 is not included.
- The graph has a closed circle at \( x = 1 \), meaning the value 1 is included.
Therefore, the domain in interval notation is:
\[ (-2, 1] \]
---
For educators and students, comprehending how to identify the domain from a graph is an essential skill in algebra and precalculus courses. This example demonstrates how to interpret open and closed circles on a graph and convert visual data into interval notation.](https://content.bartleby.com/qna-images/question/ab90fdf9-da41-461c-9056-08da6acfe393/5bbe1ce3-7d5e-4d7e-ac4f-f57300554fa9/ihjuvn_processed.jpeg)
Transcribed Image Text:### Understanding the Domain of a Function from a Graph
Below is a graph of a function. This graph helps us visualize the behavior and scope of the function within a specific range.
#### Graph Description:
- The graph has a set of axes marked from -6 to 6 on both the x-axis and y-axis.
- The function depicted is a part of an upward-facing parabola.
- The left side of the parabola starts just below the y-axis at the point (-2, -1), denoted with an open circle, indicating that this point is not included in the function.
- The right side of the parabola ends at the point (1, 1), marked with a closed circle, indicating that this point is included in the function.
- The lowest point of the curve, or vertex, appears to be at around (-0.5, -2).
#### Task:
**Write the domain of the function using interval notation.**
The domain of a function includes all possible input values (x-values) that the function can accept. Based on the given graph, the function starts at \( x = -2 \) and ends at \( x = 1 \).
- Since the graph has an open circle at \( x = -2 \), the value -2 is not included.
- The graph has a closed circle at \( x = 1 \), meaning the value 1 is included.
Therefore, the domain in interval notation is:
\[ (-2, 1] \]
---
For educators and students, comprehending how to identify the domain from a graph is an essential skill in algebra and precalculus courses. This example demonstrates how to interpret open and closed circles on a graph and convert visual data into interval notation.
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