Math  /  Algebra

Question¬\neg \sim
E 0 0 0 0 0 0 0 0 x 0 0 0 0 \square \square ( \begin{tabular}{l} \qquad \\ \hline \\ 0 \\ \cdots \\ \infty \\ \infty \end{tabular}

Studdy Solution

STEP 1

1. The given relation is a set of ordered pairs: {(2,8),(12,3),(c,4),(1,8),(0,3)}\{(2, 8), (12, 3), (c, 4), (-1, 8), (0, 3)\}.
2. For the relation to be a function, each input (first element of the ordered pairs) must correspond to exactly one output (second element of the ordered pairs).
3. We need to ensure that no input value is repeated among the ordered pairs to satisfy the definition of a function.

STEP 2

1. Extract and list the first elements (input values) from each ordered pair.
2. Identify the condition that makes the relation a function.
3. Check each provided answer choice for cc to see if it results in a repeated input value.
4. Determine the correct value of cc that ensures the relation is a function.

STEP 3

Extract the first elements (input values) from each ordered pair in the relation:
{2,12,c,1,0} \{2, 12, c, -1, 0\}

STEP 4

For the relation to be a function, these input values must be unique.
Review the current set of input values and list the given options for cc: -1, 12, 1, and 2.

STEP 5

Check the answer choice c=1c = -1:
If c=1c = -1, the set of input values becomes:
{2,12,1,1,0} \{2, 12, -1, -1, 0\}
Since 1-1 is repeated, this does not form a function.

STEP 6

Check the answer choice c=12c = 12:
If c=12c = 12, the set of input values becomes:
{2,12,12,1,0} \{2, 12, 12, -1, 0\}
Since 1212 is repeated, this does not form a function.

STEP 7

Check the answer choice c=1c = 1:
If c=1c = 1, the set of input values becomes:
{2,12,1,1,0} \{2, 12, 1, -1, 0\}
Since all values are unique, this forms a function.

STEP 8

Check the answer choice c=2c = 2:
If c=2c = 2, the set of input values becomes:
{2,12,2,1,0} \{2, 12, 2, -1, 0\}
Since 22 is repeated, this does not form a function.

STEP 9

The correct value of cc that ensures the relation is a function is:
c=1 c = 1
Solution: c=1c = 1

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