4. These tables correspond to inputs and outputs. Which of these input and output tables could represent a function rule, and which ones could not? Explain or show your reasoning. Table A: Table B: Input Output Input Output -2 4 4 -2 -1 1 1 -1 0 0 0 0 1 1 1 1 2 4 4 2 Table C: Table D: Input Output Input Output 1 0 0 1 2 0 0 2 3 0 0 3
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Table A: Input Output 1 3 2 6 3 9 In this table, each input value has a unique output value. For example, when the input is 1, the output is 3. When the input is 2, the output is 6. Show more…
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These tables correspond to inputs and outputs. Which of these input and output tables could represent a function rule, and which ones could not? Explain or show your reasoning. Table A: Table B: \begin{tabular}{|c|c|} \hline input & output \\ \hline$-2$ & 4 \\ \hline$-1$ & 1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 4 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline input & output \\ \hline 4 & $-2$ \\ \hline 1 & $-1$ \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 4 & 2 \\ \hline \end{tabular} Table $C:$ Table D: \begin{tabular}{|c|c|} \hline input & output \\ \hline 1 & 0 \\ \hline 2 & 0 \\ \hline 3 & 0 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline input & output \\ \hline 0 & 1 \\ \hline 0 & 2 \\ \hline 0 & 3 \\ \hline \end{tabular}
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Which table does not represent a function? $$ \begin{aligned} &(A)\\ &\begin{array}{|c|c|} \hline \text { input } & {\text { Output }} \\ \hline 1 & {3} \\ \hline 2 & {3} \\ \hline 3 & {3} \\ \hline 4 & {3} \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &(B)\\ &\begin{array}{|c|c|} \hline \text { input } & {\text { Output }} \\ \hline 1 & {2} \\ \hline 2 & {4} \\ \hline 3 & {6} \\ \hline 4 & {8} \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &\mathbf{C}\\ &\begin{array}{|c|c|} \hline \text { Input } & {\text { Output }} \\ \hline 5 & {4} \\ \hline 6 & {4} \\ \hline 7 & {5} \\ \hline 8 & {5} \\ \hline \end{array} \end{aligned} $$ $$ \begin{aligned} &(\mathbf{D})\\ &\begin{array}{|c|c|} \hline \text { Input } & {\text { Output }} \\ \hline 5 & {1} \\ \hline 5 & {3} \\ \hline 6 & {1} \\ \hline 6 & {3} \\ \hline \end{array} \end{aligned} $$
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In which of the relations represented by the tables below is the output a function of the input? Select all correct answers; Select all that apply:
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