Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
Sure! Let's break down the function [tex]\( f(x) = \sqrt{x - 5} - 1 \)[/tex] and complete a data table for specific values of [tex]\( x \)[/tex]. We'll use the values [tex]\( x = 6, 7, 8, 9, \)[/tex] and [tex]\( 10 \)[/tex].
### Step-by-Step Calculation:
1. When [tex]\( x = 6 \)[/tex]:
[tex]\[ f(6) = \sqrt{6 - 5} - 1 = \sqrt{1} - 1 = 1 - 1 = 0 \][/tex]
This gives the point [tex]\((6, 0)\)[/tex].
2. When [tex]\( x = 7 \)[/tex]:
[tex]\[ f(7) = \sqrt{7 - 5} - 1 = \sqrt{2} - 1 \approx 1.4142135623730951 - 1 \approx 0.41421356237309515 \][/tex]
This gives the point [tex]\((7, 0.41421356237309515)\)[/tex].
3. When [tex]\( x = 8 \)[/tex]:
[tex]\[ f(8) = \sqrt{8 - 5} - 1 = \sqrt{3} - 1 \approx 1.7320508075688772 - 1 \approx 0.7320508075688772 \][/tex]
This gives the point [tex]\((8, 0.7320508075688772)\)[/tex].
4. When [tex]\( x = 9 \)[/tex]:
[tex]\[ f(9) = \sqrt{9 - 5} - 1 = \sqrt{4} - 1 = 2 - 1 = 1 \][/tex]
This gives the point [tex]\((9, 1)\)[/tex].
5. When [tex]\( x = 10 \)[/tex]:
[tex]\[ f(10) = \sqrt{10 - 5} - 1 = \sqrt{5} - 1 \approx 2.23606797749979 - 1 \approx 1.2360679774997898 \][/tex]
This gives the point [tex]\((10, 1.2360679774997898)\)[/tex].
### Data Table:
Combining all the points we've calculated:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline 6 & 0.0 \\ 7 & 0.41421356237309515 \\ 8 & 0.7320508075688772 \\ 9 & 1.0 \\ 10 & 1.2360679774997898 \\ \hline \end{array} \][/tex]
Thus, the completed data table for the function [tex]\( f(x) = \sqrt{x - 5} - 1 \)[/tex] is:
[tex]\[ \begin{array}{c c} x & f(x) \\ \hline 6 & 0.0 \\ 7 & 0.41421356237309515 \\ 8 & 0.7320508075688772 \\ 9 & 1.0 \\ 10 & 1.2360679774997898 \\ \end{array} \][/tex]
### Step-by-Step Calculation:
1. When [tex]\( x = 6 \)[/tex]:
[tex]\[ f(6) = \sqrt{6 - 5} - 1 = \sqrt{1} - 1 = 1 - 1 = 0 \][/tex]
This gives the point [tex]\((6, 0)\)[/tex].
2. When [tex]\( x = 7 \)[/tex]:
[tex]\[ f(7) = \sqrt{7 - 5} - 1 = \sqrt{2} - 1 \approx 1.4142135623730951 - 1 \approx 0.41421356237309515 \][/tex]
This gives the point [tex]\((7, 0.41421356237309515)\)[/tex].
3. When [tex]\( x = 8 \)[/tex]:
[tex]\[ f(8) = \sqrt{8 - 5} - 1 = \sqrt{3} - 1 \approx 1.7320508075688772 - 1 \approx 0.7320508075688772 \][/tex]
This gives the point [tex]\((8, 0.7320508075688772)\)[/tex].
4. When [tex]\( x = 9 \)[/tex]:
[tex]\[ f(9) = \sqrt{9 - 5} - 1 = \sqrt{4} - 1 = 2 - 1 = 1 \][/tex]
This gives the point [tex]\((9, 1)\)[/tex].
5. When [tex]\( x = 10 \)[/tex]:
[tex]\[ f(10) = \sqrt{10 - 5} - 1 = \sqrt{5} - 1 \approx 2.23606797749979 - 1 \approx 1.2360679774997898 \][/tex]
This gives the point [tex]\((10, 1.2360679774997898)\)[/tex].
### Data Table:
Combining all the points we've calculated:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline 6 & 0.0 \\ 7 & 0.41421356237309515 \\ 8 & 0.7320508075688772 \\ 9 & 1.0 \\ 10 & 1.2360679774997898 \\ \hline \end{array} \][/tex]
Thus, the completed data table for the function [tex]\( f(x) = \sqrt{x - 5} - 1 \)[/tex] is:
[tex]\[ \begin{array}{c c} x & f(x) \\ \hline 6 & 0.0 \\ 7 & 0.41421356237309515 \\ 8 & 0.7320508075688772 \\ 9 & 1.0 \\ 10 & 1.2360679774997898 \\ \end{array} \][/tex]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.