Math  /  Algebra

Question11. Lucy examined the table of values to determine which points to add to ensure the relations remain a function. Select all the points to be added. A. (2,0)(2,0) B. (0,2)(0,2) C. (4,0)(4,0) D. (1,4)(1,4) E. (5,9)(5,9) \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-1 & 2 \\ \hline 0 & 3 \\ \hline 1 & 4 \\ \hline 2 & 5 \\ \hline 3 & 6 \\ \hline?? & ?? \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The given table represents a function, meaning each input xx must map to exactly one output yy.
2. We need to determine which of the provided points can be added without violating the definition of a function.
3. Each xx value in the table must be unique to ensure the relation remains a function.

STEP 2

1. Identify the existing xx values in the table.
2. Check each provided point (x,y)(x, y) to see if the xx value already exists in the table.
3. Select the points with xx values that do not already exist in the table.

STEP 3

Identify the existing xx values in the table.
The given table has the following xx values: 1,0,1,2,3 -1, 0, 1, 2, 3

STEP 4

Check each provided point to see if the xx value already exists in the table.
Given points: A. (2,0)(2,0): x=2x=2 (already in the table) B. (0,2)(0,2): x=0x=0 (already in the table) C. (4,0)(4,0): x=4x=4 (not in the table) D. (1,4)(1,4): x=1x=1 (already in the table) E. (5,9)(5,9): x=5x=5 (not in the table)

STEP 5

Select the points with xx values that do not already exist in the table.
The points that can be added without duplicating an xx value are: C. (4,0)(4,0) E. (5,9)(5,9)
Solution: The points that can be added to ensure the relations remain a function are: C. (4,0) and E. (5,9) \text{C. } (4,0) \text{ and E. } (5,9)

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