To determine which table could be used with Table A to verify that the function modeling Fahrenheit temperature, \(F(C)\), based on a given Celsius temperature, \(C\), is the inverse of \(C(F)\), we need to identify a table where \(F(C)\) essentially reverses the mappings provided by \(C(F)\) in Table A.
Given Table A:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
F & -4 & 5 & 23 \\
\hline
C(F) & -20 & -15 & -5 \\
\hline
\end{tabular}
\][/tex]
We need to check which table accurately represents the inverse function \(F(C)\) such that it converts the Celsius temperatures back to the original Fahrenheit temperatures:
Option 1:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
C & -20 & -15 & -5 \\
\hline
F(C) & -4 & 5 & 23 \\
\hline
\end{tabular}
\][/tex]
This table shows:
- \(F(-20) = -4\)
- \(F(-15) = 5\)
- \(F(-5) = 23\)
This precisely reverses the mappings given in Table A.
Option 2:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
C & -20 & -15 & -5 \\
\hline
F(C) & 23 & 5 & -4 \\
\hline
\end{tabular}
\][/tex]
This table shows:
- \(F(-20) = 23\)
- \(F(-15) = 5\)
- \(F(-5) = -4\)
This does not reverse the mappings correctly as \(F(-20) = 23\) and \(F(-5) = -4\) contradict our initial table.
Option 3:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
C & -20 & -15 & -5 \\
\hline
F(C) & 4 & -5 & -23 \\
\hline
\end{tabular}
\][/tex]
This table shows:
- \(F(-20) = 4\)
- \(F(-15) = -5\)
- \(F(-5) = -23\)
This also does not reverse the mappings as all the values of \(F(C)\) are incorrect.
Option 4:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
C & -20 & -15 & -5 \\
\hline
F(C) & -23 & -5 & 4 \\
\hline
\end{tabular}
\][/tex]
This table shows:
- \(F(-20) = -23\)
- \(F(-15) = -5\)
- \(F(-5) = 4\)
This does not correctly reverse the mappings either.
Thus, the table that correctly verifies \(F(C)\) as the inverse of \(C(F)\) from Table A is the first option:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
C & -20 & -15 & -5 \\
\hline
F(C) & -4 & 5 & 23 \\
\hline
\end{tabular}
\][/tex]
