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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Part e.
![The graph of a function \( h \) is given.
### Graph Analysis
The graph plotted is a curve representing the function \( h(x) \) on the coordinate plane, with the x-axis ranging from -6 to 6 and the y-axis ranging from -6 to 6. Key points on the curve corresponding to specific x-values are provided for further analysis.
### Questions and Answers
#### (a) Evaluate the function at specific points.
Find \( h(-2) \), \( h(0) \), \( h(2) \), and \( h(3) \).
- \( h(-2) = 2 \)
- \( h(0) = -2 \)
- \( h(2) = 3 \)
- \( h(3) = 4 \)
#### (b) Determine the domain and range of the function (use interval notation).
- **Domain:** \((-3, 4)\)
- **Range:** \((-2, 4)\)
#### (c) Identify \( x \) values where \( h(x) = 3 \).
- \( x = 2 \)
#### (d) Identify \( x \) values where \( h(x) \leq 3 \).
The options provided include various intervals. Select the correct interval.
- \(\boxed{[-3, 2] \text{ and } 4}\)
#### (e) Calculate the net change in \( h \) between \( x = -3 \) and \( x = 3 \).
Instructions provided do not have answer spaces below; however, the concept involves subtracting the value of the function at \( x = -3 \) from the value at \( x = 3 \).
### Detailed Explanation of Graph:
The graph shows the behavior of the function \( h(x) \) within the specified range. Key turning points and intersections with both axes offer insights into the function's characteristics. The given tasks required identifying values at specific points, intervals for domain and range, specific value solutions, and evaluating conditions for inequalities.
This problem set tests understanding of reading and interpreting graphs, evaluating functions, and understanding the concepts of domain and range, as well as inequalities in the context of graph function and analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F429fd668-1075-4973-8e47-64e8dad266df%2F8f6757c1-69dc-4f1b-b0e2-76b52ba3ba5e%2Fq1zbtdr_processed.png&w=3840&q=75)
Transcribed Image Text:The graph of a function \( h \) is given.
### Graph Analysis
The graph plotted is a curve representing the function \( h(x) \) on the coordinate plane, with the x-axis ranging from -6 to 6 and the y-axis ranging from -6 to 6. Key points on the curve corresponding to specific x-values are provided for further analysis.
### Questions and Answers
#### (a) Evaluate the function at specific points.
Find \( h(-2) \), \( h(0) \), \( h(2) \), and \( h(3) \).
- \( h(-2) = 2 \)
- \( h(0) = -2 \)
- \( h(2) = 3 \)
- \( h(3) = 4 \)
#### (b) Determine the domain and range of the function (use interval notation).
- **Domain:** \((-3, 4)\)
- **Range:** \((-2, 4)\)
#### (c) Identify \( x \) values where \( h(x) = 3 \).
- \( x = 2 \)
#### (d) Identify \( x \) values where \( h(x) \leq 3 \).
The options provided include various intervals. Select the correct interval.
- \(\boxed{[-3, 2] \text{ and } 4}\)
#### (e) Calculate the net change in \( h \) between \( x = -3 \) and \( x = 3 \).
Instructions provided do not have answer spaces below; however, the concept involves subtracting the value of the function at \( x = -3 \) from the value at \( x = 3 \).
### Detailed Explanation of Graph:
The graph shows the behavior of the function \( h(x) \) within the specified range. Key turning points and intersections with both axes offer insights into the function's characteristics. The given tasks required identifying values at specific points, intervals for domain and range, specific value solutions, and evaluating conditions for inequalities.
This problem set tests understanding of reading and interpreting graphs, evaluating functions, and understanding the concepts of domain and range, as well as inequalities in the context of graph function and analysis.
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