Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To analyze the given table and compare the characteristics of the functions, let's break down each statement:
1. [tex]$f(x)$[/tex] has an all negative domain.
- Explanation: The domain here refers to the set of all input values [tex]\( x \)[/tex]. From the table, the domain values are [tex]\(-2, -1, 1, 2\)[/tex]. There are positive numbers in this domain ([tex]\(1\)[/tex] and [tex]\(2\)[/tex]), hence [tex]\(f(x)\)[/tex] does not have an all negative domain.
- Conclusion: This statement is false.
2. [tex]$g(x)$[/tex] has the greatest maximum value.
- Explanation: To determine the maximum value of each function:
- Maximum of [tex]\(f(x)\)[/tex] = 6
- Maximum of [tex]\(g(x)\)[/tex] = 8
- Maximum of [tex]\(h(x)\)[/tex], considering the given values, is [tex]\(-1.5\)[/tex]
- [tex]\(g(x)\)[/tex] indeed has the highest maximum value among the functions.
- Conclusion: This statement is true.
3. All three functions share the same range.
- Explanation: The ranges of the functions, from the table, are:
- Range of [tex]\(f(x)\)[/tex]: \{4, 4.5, 5.5, 6\}
- Range of [tex]\(g(x)\)[/tex]: \{6, 6.5, 7.5, 8\}
- Range of [tex]\(h(x)\)[/tex]: \{-3, -2.5, -1.5\}
- The ranges are different for each function.
- Conclusion: This statement is false.
4. [tex]$h(x)$[/tex] has a range of all negative numbers.
- Explanation: Using the given values:
- The range of [tex]\(h(x)\)[/tex] is \{-3, -2.5, -1.5\}, which are all negative numbers.
- Conclusion: This statement is true.
5. All three functions share the same domain.
- Explanation: The domain for all three functions is indeed the set of [tex]\( x \)[/tex] values presented in the table, which are [tex]\(-2, -1, 1, 2\)[/tex].
- Conclusion: This statement is true.
From these observations, the two correct statements that can be used to compare the characteristics of the functions are:
4. [tex]$h(x)$[/tex] has a range of all negative numbers.
5. All three functions share the same domain.
Thus, the selected options are:
- [tex]$h(x)$[/tex] has a range of all negative numbers.
- All three functions share the same domain.
1. [tex]$f(x)$[/tex] has an all negative domain.
- Explanation: The domain here refers to the set of all input values [tex]\( x \)[/tex]. From the table, the domain values are [tex]\(-2, -1, 1, 2\)[/tex]. There are positive numbers in this domain ([tex]\(1\)[/tex] and [tex]\(2\)[/tex]), hence [tex]\(f(x)\)[/tex] does not have an all negative domain.
- Conclusion: This statement is false.
2. [tex]$g(x)$[/tex] has the greatest maximum value.
- Explanation: To determine the maximum value of each function:
- Maximum of [tex]\(f(x)\)[/tex] = 6
- Maximum of [tex]\(g(x)\)[/tex] = 8
- Maximum of [tex]\(h(x)\)[/tex], considering the given values, is [tex]\(-1.5\)[/tex]
- [tex]\(g(x)\)[/tex] indeed has the highest maximum value among the functions.
- Conclusion: This statement is true.
3. All three functions share the same range.
- Explanation: The ranges of the functions, from the table, are:
- Range of [tex]\(f(x)\)[/tex]: \{4, 4.5, 5.5, 6\}
- Range of [tex]\(g(x)\)[/tex]: \{6, 6.5, 7.5, 8\}
- Range of [tex]\(h(x)\)[/tex]: \{-3, -2.5, -1.5\}
- The ranges are different for each function.
- Conclusion: This statement is false.
4. [tex]$h(x)$[/tex] has a range of all negative numbers.
- Explanation: Using the given values:
- The range of [tex]\(h(x)\)[/tex] is \{-3, -2.5, -1.5\}, which are all negative numbers.
- Conclusion: This statement is true.
5. All three functions share the same domain.
- Explanation: The domain for all three functions is indeed the set of [tex]\( x \)[/tex] values presented in the table, which are [tex]\(-2, -1, 1, 2\)[/tex].
- Conclusion: This statement is true.
From these observations, the two correct statements that can be used to compare the characteristics of the functions are:
4. [tex]$h(x)$[/tex] has a range of all negative numbers.
5. All three functions share the same domain.
Thus, the selected options are:
- [tex]$h(x)$[/tex] has a range of all negative numbers.
- All three functions share the same domain.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
