Math  /  Discrete

QuestionA) State whether each set of ordered pairs represents a function. 1) {(10,9),(2,16),(6,7),(5,8),(8,16),(11,9)}\{(10,9),(-2,-16),(-6,7),(5,8),(8,-16),(-11,9)\} \qquad 3) {(13,4),(7,15),(13,9),(6,12),(18,0)}\{(-13,4),(7,-15),(-13,9),(6,-12),(-18,0)\} \qquad 5) {(4,3),(5,9),(11,4),(9,6),(5,3),(8,9),(1,4)}\{(-4,3),(5,-9),(11,4),(9,6),(5,-3),(8,-9),(1,4)\} \qquad 7) {(6,0),(12,16),(6,10),(20,7)}\{(6,0),(-12,-16),(-6,10),(20,-7)\} 2) {(7,4),(8,3),(7,7),(20,8),(5,9),(3,1),(2,6)}\{(-7,4),(-8,3),(-7,7),(-20,8),(5,9),(3,1),(2,6)\} \qquad 4) {(15,3),(6,9),(3,0),(1,16)}\{(15,-3),(-6,9),(-3,0),(-1,16)\} \qquad 6) {(12,18),(15,1),(12,5),(0,9),(5,17)}\{(12,-18),(15,1),(12,5),(0,9),(-5,-17)\} \qquad 8) {(2,4),(8,3),(7,4),(2,8),(11,8),(9,4\{(-2,-4),(-8,3),(-7,-4),(-2,-8),(11,8),(9,-4

Studdy Solution

STEP 1

1. A function is defined as a relation where each input (first element of the ordered pair) is associated with exactly one output (second element of the ordered pair).
2. We need to determine if each set of ordered pairs represents a function based on the definition above.

STEP 2

1. Examine each set of ordered pairs.
2. Determine if any input value is repeated with a different output.
3. Conclude whether each set represents a function.

STEP 3

Examine set 1: {(10,9),(2,16),(6,7),(5,8),(8,16),(11,9)}\{(10,9),(-2,-16),(-6,7),(5,8),(8,-16),(-11,9)\}.
- Check if any first elements (inputs) are repeated with different second elements (outputs).

STEP 4

For set 1, no inputs are repeated with different outputs. Therefore, set 1 represents a function.

STEP 5

Examine set 2: {(7,4),(8,3),(7,7),(20,8),(5,9),(3,1),(2,6)}\{(-7,4),(-8,3),(-7,7),(-20,8),(5,9),(3,1),(2,6)\}.
- Check if any inputs are repeated with different outputs.

STEP 6

For set 2, the input 7-7 is repeated with different outputs 44 and 77. Therefore, set 2 does not represent a function.

STEP 7

Examine set 3: {(13,4),(7,15),(13,9),(6,12),(18,0)}\{(-13,4),(7,-15),(-13,9),(6,-12),(-18,0)\}.
- Check if any inputs are repeated with different outputs.

STEP 8

For set 3, the input 13-13 is repeated with different outputs 44 and 99. Therefore, set 3 does not represent a function.

STEP 9

Examine set 4: {(15,3),(6,9),(3,0),(1,16)}\{(15,-3),(-6,9),(-3,0),(-1,16)\}.
- Check if any inputs are repeated with different outputs.

STEP 10

For set 4, no inputs are repeated with different outputs. Therefore, set 4 represents a function.

STEP 11

Examine set 5: {(4,3),(5,9),(11,4),(9,6),(5,3),(8,9),(1,4)}\{(-4,3),(5,-9),(11,4),(9,6),(5,-3),(8,-9),(1,4)\}.
- Check if any inputs are repeated with different outputs.

STEP 12

For set 5, the input 55 is repeated with different outputs 9-9 and 3-3. Therefore, set 5 does not represent a function.

STEP 13

Examine set 6: {(12,18),(15,1),(12,5),(0,9),(5,17)}\{(12,-18),(15,1),(12,5),(0,9),(-5,-17)\}.
- Check if any inputs are repeated with different outputs.

STEP 14

For set 6, the input 1212 is repeated with different outputs 18-18 and 55. Therefore, set 6 does not represent a function.

STEP 15

Examine set 7: {(6,0),(12,16),(6,10),(20,7)}\{(6,0),(-12,-16),(-6,10),(20,-7)\}.
- Check if any inputs are repeated with different outputs.

STEP 16

For set 7, no inputs are repeated with different outputs. Therefore, set 7 represents a function.

STEP 17

Examine set 8: {(2,4),(8,3),(7,4),(2,8),(11,8),(9,4)}\{(-2,-4),(-8,3),(-7,-4),(-2,-8),(11,8),(9,-4)\}.
- Check if any inputs are repeated with different outputs.

STEP 18

For set 8, the input 2-2 is repeated with different outputs 4-4 and 8-8. Therefore, set 8 does not represent a function.
The results for each set are as follows: 1) Function 2) Not a function 3) Not a function 4) Function 5) Not a function 6) Not a function 7) Function 8) Not a function

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