IDNLearn.com provides a reliable platform for finding accurate and timely answers. Our experts are available to provide in-depth and trustworthy answers to any questions you may have.
Sagot :
To determine which table of values contains points that lie on the graph of the function [tex]\( f(x) = \sqrt{x} \)[/tex], we need to evaluate the function at each [tex]\( x \)[/tex]-value given in both tables and check which points correspond correctly to the values of [tex]\( f(x) \)[/tex].
### Evaluating [tex]\( f(x) = \sqrt{x} \)[/tex]
For the points in the first table:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -1 & 1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 4 & 16 \\ \hline \end{array} \][/tex]
1. [tex]\( f(-1) = \sqrt{-1} \)[/tex]: This results in a complex number [tex]\( (6.123233995736766e-17+1j) \)[/tex], which does not lie on the real graph of [tex]\( \sqrt{x} \)[/tex].
2. [tex]\( f(0) = \sqrt{0} = 0 \)[/tex]: Correct, as [tex]\((0, 0)\)[/tex] lies on the graph of [tex]\( y = \sqrt{x} \)[/tex].
3. [tex]\( f(1) = \sqrt{1} = 1 \)[/tex]: Correct, as [tex]\((1, 1)\)[/tex] lies on the graph of [tex]\( y = \sqrt{x} \)[/tex].
4. [tex]\( f(4) = \sqrt{4} = 2 \)[/tex]: The value [tex]\( f(4) = 16 \)[/tex] given in the table is incorrect. [tex]\((4, 2)\)[/tex] should be the correct point on the graph.
Hence, the first table does not correctly represent the function [tex]\( f(x) = \sqrt{x} \)[/tex].
For the points in the second table:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -1 & 0 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 4 & 2 \\ \hline \end{array} \][/tex]
1. [tex]\( f(-1) = \sqrt{-1} \)[/tex]: Again, this results in a complex number [tex]\( (6.123233995736766e-17+1j) \)[/tex], which does not lie on the real graph of [tex]\( \sqrt{x} \)[/tex].
2. [tex]\( f(0) = \sqrt{0} = 0 \)[/tex]: Correct, as [tex]\((0, 0)\)[/tex] lies on the graph of [tex]\( y = \sqrt{x} \)[/tex].
3. [tex]\( f(1) = \sqrt{1} = 1 \)[/tex]: Correct, as [tex]\((1, 1)\)[/tex] lies on the graph of [tex]\( y = \sqrt{x} \)[/tex].
4. [tex]\( f(4) = \sqrt{4} = 2 \)[/tex]: Correct, as [tex]\((4, 2)\)[/tex] lies on the graph of [tex]\( y = \sqrt{x} \)[/tex].
Thus, except for the complex number calculated for [tex]\(f(-1)\)[/tex] which is not on the graph, all other points in the second table correctly represent the values of the function [tex]\( f(x) = \sqrt{x} \)[/tex].
### Conclusion
By evaluating [tex]\( f(x) = \sqrt{x} \)[/tex] for the given points, we find that the second table correctly contains points that lie on the graph of the function, except for x = -1. Thus, with this understanding, it is clear that:
- The second table ([tex]\( x \)[/tex] values like [tex]\(0, 1, 4 \)[/tex]) correctly represents the real-valued points on the graph of [tex]\( f(x) \)[/tex].
### Evaluating [tex]\( f(x) = \sqrt{x} \)[/tex]
For the points in the first table:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -1 & 1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 4 & 16 \\ \hline \end{array} \][/tex]
1. [tex]\( f(-1) = \sqrt{-1} \)[/tex]: This results in a complex number [tex]\( (6.123233995736766e-17+1j) \)[/tex], which does not lie on the real graph of [tex]\( \sqrt{x} \)[/tex].
2. [tex]\( f(0) = \sqrt{0} = 0 \)[/tex]: Correct, as [tex]\((0, 0)\)[/tex] lies on the graph of [tex]\( y = \sqrt{x} \)[/tex].
3. [tex]\( f(1) = \sqrt{1} = 1 \)[/tex]: Correct, as [tex]\((1, 1)\)[/tex] lies on the graph of [tex]\( y = \sqrt{x} \)[/tex].
4. [tex]\( f(4) = \sqrt{4} = 2 \)[/tex]: The value [tex]\( f(4) = 16 \)[/tex] given in the table is incorrect. [tex]\((4, 2)\)[/tex] should be the correct point on the graph.
Hence, the first table does not correctly represent the function [tex]\( f(x) = \sqrt{x} \)[/tex].
For the points in the second table:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -1 & 0 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 4 & 2 \\ \hline \end{array} \][/tex]
1. [tex]\( f(-1) = \sqrt{-1} \)[/tex]: Again, this results in a complex number [tex]\( (6.123233995736766e-17+1j) \)[/tex], which does not lie on the real graph of [tex]\( \sqrt{x} \)[/tex].
2. [tex]\( f(0) = \sqrt{0} = 0 \)[/tex]: Correct, as [tex]\((0, 0)\)[/tex] lies on the graph of [tex]\( y = \sqrt{x} \)[/tex].
3. [tex]\( f(1) = \sqrt{1} = 1 \)[/tex]: Correct, as [tex]\((1, 1)\)[/tex] lies on the graph of [tex]\( y = \sqrt{x} \)[/tex].
4. [tex]\( f(4) = \sqrt{4} = 2 \)[/tex]: Correct, as [tex]\((4, 2)\)[/tex] lies on the graph of [tex]\( y = \sqrt{x} \)[/tex].
Thus, except for the complex number calculated for [tex]\(f(-1)\)[/tex] which is not on the graph, all other points in the second table correctly represent the values of the function [tex]\( f(x) = \sqrt{x} \)[/tex].
### Conclusion
By evaluating [tex]\( f(x) = \sqrt{x} \)[/tex] for the given points, we find that the second table correctly contains points that lie on the graph of the function, except for x = -1. Thus, with this understanding, it is clear that:
- The second table ([tex]\( x \)[/tex] values like [tex]\(0, 1, 4 \)[/tex]) correctly represents the real-valued points on the graph of [tex]\( f(x) \)[/tex].
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For precise answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.
