Explore a diverse range of topics and get answers from knowledgeable individuals on IDNLearn.com. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.
Sagot :
We need to determine which of the given functions has a range that includes -4:
1. [tex]\( y = \sqrt{x} - 5 \)[/tex]
2. [tex]\( y = \sqrt{x} + 5 \)[/tex]
3. [tex]\( y = \sqrt{x+5} \)[/tex]
4. [tex]\( y = \sqrt{x-5} \)[/tex]
We are given [tex]\(x = 59.0\)[/tex]. Let's compute the values for each function and see where -4 falls within the range.
First, calculate [tex]\( \sqrt{59} \)[/tex]:
[tex]\[ \sqrt{59} \approx 7.681145747868608 \][/tex]
Using this value, compute:
1. [tex]\( y = \sqrt{59} - 5 \)[/tex]
[tex]\[ y = 7.681145747868608 - 5 = 2.681145747868608 \][/tex]
The result is approximately [tex]\(2.681\)[/tex].
2. [tex]\( y = \sqrt{59} + 5 \)[/tex]
[tex]\[ y = 7.681145747868608 + 5 = 12.681145747868609 \][/tex]
The result is approximately [tex]\(12.681\)[/tex].
For the next two functions, we need to adjust the argument inside the square root:
3. [tex]\( y = \sqrt{59 + 5} = \sqrt{64} \)[/tex]
[tex]\[ y = \sqrt{64} = 8 \][/tex]
The result is [tex]\(8\)[/tex].
4. [tex]\( y = \sqrt{59 - 5} = \sqrt{54} \)[/tex]
[tex]\[ y = \sqrt{54} \approx 7.3484692283495345 \][/tex]
The result is approximately [tex]\(7.348\)[/tex].
Now, let's look at the ranges of these functions to see if -4 is included:
1. For [tex]\( y = \sqrt{59} - 5 \)[/tex], the range is given as approximately [tex]\(2.681\)[/tex], which does not include -4.
2. For [tex]\( y = \sqrt{59} + 5 \)[/tex], the range is given as approximately [tex]\(12.681\)[/tex], which does not include -4.
3. For [tex]\( y = \sqrt{x+5} \)[/tex], the result is [tex]\(8\)[/tex], which does not include -4.
4. For [tex]\( y = \sqrt{x-5} \)[/tex], the result is approximately [tex]\(7.348\)[/tex], which does not include -4.
Review of the functions confirms that only [tex]\( y = \sqrt{x} - 5 \)[/tex] gives a result that includes -4 in its range. Therefore, the function whose range includes -4 is:
[tex]\[ y = \sqrt{x} - 5 \][/tex]
1. [tex]\( y = \sqrt{x} - 5 \)[/tex]
2. [tex]\( y = \sqrt{x} + 5 \)[/tex]
3. [tex]\( y = \sqrt{x+5} \)[/tex]
4. [tex]\( y = \sqrt{x-5} \)[/tex]
We are given [tex]\(x = 59.0\)[/tex]. Let's compute the values for each function and see where -4 falls within the range.
First, calculate [tex]\( \sqrt{59} \)[/tex]:
[tex]\[ \sqrt{59} \approx 7.681145747868608 \][/tex]
Using this value, compute:
1. [tex]\( y = \sqrt{59} - 5 \)[/tex]
[tex]\[ y = 7.681145747868608 - 5 = 2.681145747868608 \][/tex]
The result is approximately [tex]\(2.681\)[/tex].
2. [tex]\( y = \sqrt{59} + 5 \)[/tex]
[tex]\[ y = 7.681145747868608 + 5 = 12.681145747868609 \][/tex]
The result is approximately [tex]\(12.681\)[/tex].
For the next two functions, we need to adjust the argument inside the square root:
3. [tex]\( y = \sqrt{59 + 5} = \sqrt{64} \)[/tex]
[tex]\[ y = \sqrt{64} = 8 \][/tex]
The result is [tex]\(8\)[/tex].
4. [tex]\( y = \sqrt{59 - 5} = \sqrt{54} \)[/tex]
[tex]\[ y = \sqrt{54} \approx 7.3484692283495345 \][/tex]
The result is approximately [tex]\(7.348\)[/tex].
Now, let's look at the ranges of these functions to see if -4 is included:
1. For [tex]\( y = \sqrt{59} - 5 \)[/tex], the range is given as approximately [tex]\(2.681\)[/tex], which does not include -4.
2. For [tex]\( y = \sqrt{59} + 5 \)[/tex], the range is given as approximately [tex]\(12.681\)[/tex], which does not include -4.
3. For [tex]\( y = \sqrt{x+5} \)[/tex], the result is [tex]\(8\)[/tex], which does not include -4.
4. For [tex]\( y = \sqrt{x-5} \)[/tex], the result is approximately [tex]\(7.348\)[/tex], which does not include -4.
Review of the functions confirms that only [tex]\( y = \sqrt{x} - 5 \)[/tex] gives a result that includes -4 in its range. Therefore, the function whose range includes -4 is:
[tex]\[ y = \sqrt{x} - 5 \][/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.