Math / Algebra

Question $\qquad$ 2. Which set of ordered pairs represents $y$ as a function of $x$ ? A. $\{(2,5),(3,7),(4,9),(5,11)\}$ B. $\{(-1,6),(-4,3),(0,5),(-1,8)\}$ C. $\{(0,25),(-1,17),(14,-9),(0,-3)\}$ D. $\{(-5,-5),(-5,9),(-4,-2),(-3,1)\}$

Studdy Solution

STEP 1

What is this asking? Which of these sets has exactly one $y$ value for every $x$ value? Watch out! It's easy to get tricked by similar $x$ or $y$ values, so focus on the core concept of a function: one input, one output!

STEP 2

1. Check Set A
2. Check Set B
3. Check Set C
4. Check Set D

STEP 3

Let's examine set A: $\{(2,5),(3,7),(4,9),(5,11)\}$ .
Each $x$ value (2, 3, 4, and 5) appears exactly once, and each is paired with a unique $y$ value.

STEP 4

Since each $x$ has only one $y$ , this set represents $y$ as a function of $x$ .
Woohoo!

STEP 5

Now, let's look at set B: $\{(-1,6),(-4,3),(0,5),(-1,8)\}$ .
Notice that the $x$ value $-1$ appears twice, paired with different $y$ values (6 and 8).

STEP 6

This violates the rule of functions!
One input cannot have two different outputs.
So, set B does not represent $y$ as a function of $x$ .

STEP 7

Checking set C: $\{(0,25),(-1,17),(14,-9),(0,-3)\}$ .
Here, the $x$ value $0$ appears twice, with different $y$ values (25 and -3).

STEP 8

Just like set B, this breaks the function rule.
Set C does not represent $y$ as a function of $x$ .

STEP 9

Finally, let's analyze set D: $\{(-5,-5),(-5,9),(-4,-2),(-3,1)\}$ .
The $x$ value $-5$ appears twice, paired with different $y$ values (-5 and 9).

STEP 10

Once again, this violates the function rule.
Set D does not represent $y$ as a function of $x$ .

STEP 11

Set A, $\{(2,5),(3,7),(4,9),(5,11)\}$ , is the only set that represents $y$ as a function of $x$ .
So the answer is A!

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Question $\qquad$ 2. Which set of ordered pairs represents $y$ as a function of $x$ ? A. $\{(2,5),(3,7),(4,9),(5,11)\}$ B. $\{(-1,6),(-4,3),(0,5),(-1,8)\}$ C. $\{(0,25),(-1,17),(14,-9),(0,-3)\}$ D. $\{(-5,-5),(-5,9),(-4,-2),(-3,1)\}$

Studdy Solution

STEP 1

What is this asking? Which of these sets has exactly one $y$ value for every $x$ value? Watch out! It's easy to get tricked by similar $x$ or $y$ values, so focus on the core concept of a function: one input, one output!

STEP 2

1. Check Set A
2. Check Set B
3. Check Set C
4. Check Set D

STEP 3

Let's examine set A: $\{(2,5),(3,7),(4,9),(5,11)\}$ .
Each $x$ value (2, 3, 4, and 5) appears exactly once, and each is paired with a unique $y$ value.

STEP 4

Since each $x$ has only one $y$ , this set represents $y$ as a function of $x$ .
Woohoo!

STEP 5

Now, let's look at set B: $\{(-1,6),(-4,3),(0,5),(-1,8)\}$ .
Notice that the $x$ value $-1$ appears twice, paired with different $y$ values (6 and 8).

STEP 6

This violates the rule of functions!
One input cannot have two different outputs.
So, set B does not represent $y$ as a function of $x$ .

STEP 7

Checking set C: $\{(0,25),(-1,17),(14,-9),(0,-3)\}$ .
Here, the $x$ value $0$ appears twice, with different $y$ values (25 and -3).

STEP 8

Just like set B, this breaks the function rule.
Set C does not represent $y$ as a function of $x$ .

STEP 9

Finally, let's analyze set D: $\{(-5,-5),(-5,9),(-4,-2),(-3,1)\}$ .
The $x$ value $-5$ appears twice, paired with different $y$ values (-5 and 9).

STEP 10

Once again, this violates the function rule.
Set D does not represent $y$ as a function of $x$ .

STEP 11

Set A, $\{(2,5),(3,7),(4,9),(5,11)\}$ , is the only set that represents $y$ as a function of $x$ .
So the answer is A!

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Studdy Solution

STEP 1

What is this asking? Which of these sets has exactly one yyy value for every xxx value? Watch out! It's easy to get tricked by similar xxx or yyy values, so focus on the core concept of a function: one input, one output!

STEP 2

1. Check Set A2. Check Set B3. Check Set C4. Check Set D

STEP 3

Let's **examine** set A: {(2,5),(3,7),(4,9),(5,11)}\{(2,5),(3,7),(4,9),(5,11)\}{(2,5),(3,7),(4,9),(5,11)}.Each xxx value (2, 3, 4, and 5) appears **exactly once**, and each is paired with a **unique** yyy value.

STEP 4

Since each xxx has only one yyy, this set **represents** yyy as a function of xxx.Woohoo!

STEP 5

Now, let's **look** at set B: {(−1,6),(−4,3),(0,5),(−1,8)}\{(-1,6),(-4,3),(0,5),(-1,8)\}{(−1,6),(−4,3),(0,5),(−1,8)}.Notice that the xxx value −1-1−1 appears **twice**, paired with *different* yyy values (6 and 8).

STEP 6

This **violates** the rule of functions!One input cannot have two different outputs.So, set B **does not** represent yyy as a function of xxx.

STEP 7

**Checking** set C: {(0,25),(−1,17),(14,−9),(0,−3)}\{(0,25),(-1,17),(14,-9),(0,-3)\}{(0,25),(−1,17),(14,−9),(0,−3)}.Here, the xxx value 000 appears **twice**, with different yyy values (25 and -3).

STEP 8

Just like set B, this **breaks** the function rule.Set C **does not** represent yyy as a function of xxx.

STEP 9

Finally, let's **analyze** set D: {(−5,−5),(−5,9),(−4,−2),(−3,1)}\{(-5,-5),(-5,9),(-4,-2),(-3,1)\}{(−5,−5),(−5,9),(−4,−2),(−3,1)}.The xxx value −5-5−5 appears **twice**, paired with different yyy values (-5 and 9).

STEP 10

Once again, this **violates** the function rule.Set D **does not** represent yyy as a function of xxx.

STEP 11

Set A, {(2,5),(3,7),(4,9),(5,11)}\{(2,5),(3,7),(4,9),(5,11)\}{(2,5),(3,7),(4,9),(5,11)}, is the **only set** that represents yyy as a function of xxx.So the answer is A!

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Studdy solves anything!

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What is this asking? Which of these sets has exactly one $y$ value for every $x$ value? Watch out! It's easy to get tricked by similar $x$ or $y$ values, so focus on the core concept of a function: one input, one output!

1. Check Set A
2. Check Set B
3. Check Set C
4. Check Set D

Let's examine set A: $\{(2,5),(3,7),(4,9),(5,11)\}$ .
Each $x$ value (2, 3, 4, and 5) appears exactly once, and each is paired with a unique $y$ value.

Since each $x$ has only one $y$ , this set represents $y$ as a function of $x$ .
Woohoo!

Now, let's look at set B: $\{(-1,6),(-4,3),(0,5),(-1,8)\}$ .
Notice that the $x$ value $-1$ appears twice, paired with different $y$ values (6 and 8).

This violates the rule of functions!
One input cannot have two different outputs.
So, set B does not represent $y$ as a function of $x$ .

Checking set C: $\{(0,25),(-1,17),(14,-9),(0,-3)\}$ .
Here, the $x$ value $0$ appears twice, with different $y$ values (25 and -3).

Just like set B, this breaks the function rule.
Set C does not represent $y$ as a function of $x$ .

Finally, let's analyze set D: $\{(-5,-5),(-5,9),(-4,-2),(-3,1)\}$ .
The $x$ value $-5$ appears twice, paired with different $y$ values (-5 and 9).

Once again, this violates the function rule.
Set D does not represent $y$ as a function of $x$ .

Set A, $\{(2,5),(3,7),(4,9),(5,11)\}$ , is the only set that represents $y$ as a function of $x$ .
So the answer is A!