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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### Analyzing the Graph
The graph provided shows a continuous function \( h \) with the following key points:
- The function starts from the point (-4, 3) and ends at the point (4, -2) on the \( x \)-axis.
### Domain
The domain of a function includes all the possible \( x \)-values that the function can take. Observing the graph:
- The \( x \)-values range from -4 to 4, although the point at \( x = 4 \) has an open circle, indicating that this \( x \)-value is not included in the domain.
Therefore, the domain of \( h \) in interval notation is:
\[ [-4, 4) \]
### Range
The range of a function includes all the possible \( y \)-values that the function can output. Observing the graph:
- The \( y \)-values range from -2 to 3, with both endpoints being included, as there are no open circles on the \( y \)-values.
Therefore, the range of \( h \) in interval notation is:
\[ [-2, 3] \]
### Conclusion
From the given graph, we have determined the domain and range of the function \( h \). The domain is all the possible \( x \)-values from -4 to just less than 4, and the range is all the possible \( y \)-values from -2 to 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f12fdb3-7ef0-45e1-9bc4-16f2ee47ff7c%2F16e2ef04-98fc-4792-83d3-d82043d3c1f7%2Fcyz426di_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:## Domain and Range from the Graph of a Continuous Function
### Understanding the Domain and Range
The entire graph of the function \( h \) is shown in the figure below. We will write the domain and range of \( h \) using interval notation.
### Analyzing the Graph
The graph provided shows a continuous function \( h \) with the following key points:
- The function starts from the point (-4, 3) and ends at the point (4, -2) on the \( x \)-axis.
### Domain
The domain of a function includes all the possible \( x \)-values that the function can take. Observing the graph:
- The \( x \)-values range from -4 to 4, although the point at \( x = 4 \) has an open circle, indicating that this \( x \)-value is not included in the domain.
Therefore, the domain of \( h \) in interval notation is:
\[ [-4, 4) \]
### Range
The range of a function includes all the possible \( y \)-values that the function can output. Observing the graph:
- The \( y \)-values range from -2 to 3, with both endpoints being included, as there are no open circles on the \( y \)-values.
Therefore, the range of \( h \) in interval notation is:
\[ [-2, 3] \]
### Conclusion
From the given graph, we have determined the domain and range of the function \( h \). The domain is all the possible \( x \)-values from -4 to just less than 4, and the range is all the possible \( y \)-values from -2 to 3.
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