Question10. True or False: Is every relation a function? For problems 15-26, check if each relation is a function and find the domain and range.
16. $\{(-2,5),(-1,3),(3,7),(4,12)\}$
20. $\{(0,-2),(1,3),(2,3),(3,7)\}$
24. $\{(-4,4),(-3,3),(-2,2),(-1,1),(-4,0)\}$

Studdy Solution

STEP 1

Assumptions1. A relation is a set of ordered pairs. . A function is a special type of relation where every element in the domain corresponds to exactly one element in the range.
3. The domain of a function or a relation is the set of all possible x-values (the first elements of the ordered pairs).
4. The range of a function or a relation is the set of all possible y-values (the second elements of the ordered pairs).

STEP 2

First, let's answer the True or False question "Every relation is a function."
This statement is False. Not every relation is a function. A relation is a function only if every element in the domain corresponds to exactly one element in the range.

STEP 3

Now, let's determine whether each relation represents a function and state the domain and range for each.
The first relation is $\{(-2,5),(-1,3),(3,7),(,12)\}$ .
To determine if this is a function, we need to check if each x-value (the first element of each ordered pair) corresponds to exactly one y-value (the second element of each ordered pair).

STEP 4

In the relation $\{(-2,),(-1,3),(3,7),(4,12)\}$ , each x-value corresponds to exactly one y-value. Therefore, this relation is a function.
The domain of this function is the set of x-values $\{-2, -1,3,4\}$ , and the range is the set of y-values $\{,3,7,12\}$ .

STEP 5

The next relation is $\{(0,-2),(1,3),(2,3),(3,7)\}$ .
Again, we need to check if each x-value corresponds to exactly one y-value.

STEP 6

In the relation $\{(0,-2),(1,3),(2,3),(3,)\}$ , each x-value corresponds to exactly one y-value. Therefore, this relation is also a function.
The domain of this function is the set of x-values $\{0,1,2,3\}$ , and the range is the set of y-values $\{-2,3,\}$ .

STEP 7

The last relation is $\{(-4,4),(-3,3),(-2,2),(-1,1),(-4,0)\}$ .
Again, we need to check if each x-value corresponds to exactly one y-value.

STEP 8

In the relation $\{(-4,4),(-3,3),(-2,2),(-1,1),(-4,0)\}$ , the x-value -4 corresponds to two different y-values (4 and0). Therefore, this relation is not a function.
The domain of this relation is the set of x-values $\{-4, -3, -2, -1\}$ , and the range is the set of y-values $\{4,3,2,1,0\}$ .

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Question10. True or False: Is every relation a function? For problems 15-26, check if each relation is a function and find the domain and range.
16. $\{(-2,5),(-1,3),(3,7),(4,12)\}$
20. $\{(0,-2),(1,3),(2,3),(3,7)\}$
24. $\{(-4,4),(-3,3),(-2,2),(-1,1),(-4,0)\}$

Studdy Solution

STEP 1

STEP 2

First, let's answer the True or False question "Every relation is a function."
This statement is False. Not every relation is a function. A relation is a function only if every element in the domain corresponds to exactly one element in the range.

STEP 3

STEP 4

In the relation $\{(-2,),(-1,3),(3,7),(4,12)\}$ , each x-value corresponds to exactly one y-value. Therefore, this relation is a function.
The domain of this function is the set of x-values $\{-2, -1,3,4\}$ , and the range is the set of y-values $\{,3,7,12\}$ .

STEP 5

The next relation is $\{(0,-2),(1,3),(2,3),(3,7)\}$ .
Again, we need to check if each x-value corresponds to exactly one y-value.

STEP 6

In the relation $\{(0,-2),(1,3),(2,3),(3,)\}$ , each x-value corresponds to exactly one y-value. Therefore, this relation is also a function.
The domain of this function is the set of x-values $\{0,1,2,3\}$ , and the range is the set of y-values $\{-2,3,\}$ .

STEP 7

The last relation is $\{(-4,4),(-3,3),(-2,2),(-1,1),(-4,0)\}$ .
Again, we need to check if each x-value corresponds to exactly one y-value.

STEP 8

In the relation $\{(-4,4),(-3,3),(-2,2),(-1,1),(-4,0)\}$ , the x-value -4 corresponds to two different y-values (4 and0). Therefore, this relation is not a function.
The domain of this relation is the set of x-values $\{-4, -3, -2, -1\}$ , and the range is the set of y-values $\{4,3,2,1,0\}$ .

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Studdy Solution

STEP 1

STEP 2

First, let's answer the True or False question "Every relation is a function."This statement is False. Not every relation is a function. A relation is a function only if every element in the domain corresponds to exactly one element in the range.

STEP 3

STEP 4

STEP 5

The next relation is {(0,−2),(1,3),(2,3),(3,7)}\{(0,-2),(1,3),(2,3),(3,7)\}{(0,−2),(1,3),(2,3),(3,7)}.Again, we need to check if each x-value corresponds to exactly one y-value.

STEP 6

STEP 7

The last relation is {(−4,4),(−3,3),(−2,2),(−1,1),(−4,0)}\{(-4,4),(-3,3),(-2,2),(-1,1),(-4,0)\}{(−4,4),(−3,3),(−2,2),(−1,1),(−4,0)}.Again, we need to check if each x-value corresponds to exactly one y-value.

STEP 8

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Studdy solves anything!

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First, let's answer the True or False question "Every relation is a function."
This statement is False. Not every relation is a function. A relation is a function only if every element in the domain corresponds to exactly one element in the range.

The next relation is $\{(0,-2),(1,3),(2,3),(3,7)\}$ .
Again, we need to check if each x-value corresponds to exactly one y-value.

The last relation is $\{(-4,4),(-3,3),(-2,2),(-1,1),(-4,0)\}$ .
Again, we need to check if each x-value corresponds to exactly one y-value.