Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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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.](https://content.bartleby.com/qna-images/question/1f12fdb3-7ef0-45e1-9bc4-16f2ee47ff7c/16e2ef04-98fc-4792-83d3-d82043d3c1f7/cyz426di_reoriented.jpeg)
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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- can you show work on how you found the domain and rangearrow_forwardFind and simplify an expression for the indicated composite functions. State the domain using interval notation. 2. a) f(x) 3x-1, g(x)Find (go f (x) Simplified Expression: (write in interval notation) Domain:arrow_forwardUse the graph of the function to find its domain and range. Write the domain and range in interval notation. Provide your answer below: domain: range: -7 36 -6 19 + -3 400 -2 8+ 7 6+ 5- 44 3- 24 1+ -10 4 -2- -3+ - - - -4- 44 1 2 +*+ 4 • toarrow_forward
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