Question

1. is the following graph a function?
2. circle graph
3. intersecting lines graph
4. scatter plot graph
5. scatter plot graph

1. are the following tables a function?

5)

x	y
3	3
-6	-11
4	-2

1. mapping diagram

6)

input	output
2	-4
4	-2
6	0

7)

input	output
5	4
7	6

1. is the following a function?
2. {(5, -1), (0, 3), (-2, -4), (6, -1), (-2, 3)}
3. {(9, 2), (-4, -1), (0, -3), (-7, 6), (5, -2)}

Explanation:

To determine if a relation is a function, we use the vertical line test for graphs (a vertical line intersects the graph at most once) and the definition of a function for tables/mappings/ordered pairs (each input has exactly one output). Let’s analyze each part:

1. Graphs (Is it a function?):

• 1) Circle: A vertical line will intersect the circle at two points. Fails the vertical line test. $\boldsymbol{\text{No}}$.
• 2) Two intersecting lines: A vertical line will intersect one of the lines at two points. Fails the vertical line test. $\boldsymbol{\text{No}}$.
• 3) Scattered points: No vertical line intersects more than one point. Passes the vertical line test. $\boldsymbol{\text{Yes}}$.
• 4) Scattered points: No vertical line intersects more than one point. Passes the vertical line test. $\boldsymbol{\text{Yes}}$.

2. Tables/Mappings (Is it a function?):

• 5) Table: Input $x=4$ has two outputs ($8$ and $-2$). Fails the “one input → one output” rule. $\boldsymbol{\text{No}}$.
• 6) Mapping (oval diagram): Input $9$ maps to two outputs, and input $-6$ maps to two outputs. Fails the “one input → one output” rule. $\boldsymbol{\text{No}}$.
• 7) Input-Output Table: Each input ($0, 2, 4, 6$) has exactly one output. Passes the rule. $\boldsymbol{\text{Yes}}$.
• 8) Input-Output Table: Inputs $3, 5, 7$ each have one output (note: $5$ and $7$ map to $4$ and $6$—multiple inputs can share an output, but each input has only one output). Passes the rule. $\boldsymbol{\text{Yes}}$.

3. Ordered Pairs (Is it a function?):

• First set: $\{(5, -1), (0, 3), (-2, -4), (6, -1), (-2, 3)\}$: Input $-2$ has two outputs ($-4$ and $3$). Fails the “one input → one output” rule. $\boldsymbol{\text{No}}$.
• Second set: $\{(9, 2), (-4, -1), (0, -3), (-7, 6), (5, -2)\}$: Each input ($9, -4, 0, -7, 5$) has exactly one output. Passes the rule. $\boldsymbol{\text{Yes}}$.

Final Answers (Summarized):

Item	Is it a function?
2)	No
3)	Yes
4)	Yes
5)	No
6)	No
7)	Yes
8)	Yes
First ordered pair set	No
Second ordered pair set	Yes

(Note: If you need only specific items, adjust based on the question’s focus. The key is applying the vertical line test or “one input → one output” rule.)

Answer:

To determine if a relation is a function, we use the vertical line test for graphs (a vertical line intersects the graph at most once) and the definition of a function for tables/mappings/ordered pairs (each input has exactly one output). Let’s analyze each part:

1. Graphs (Is it a function?):

• 1) Circle: A vertical line will intersect the circle at two points. Fails the vertical line test. $\boldsymbol{\text{No}}$.
• 2) Two intersecting lines: A vertical line will intersect one of the lines at two points. Fails the vertical line test. $\boldsymbol{\text{No}}$.
• 3) Scattered points: No vertical line intersects more than one point. Passes the vertical line test. $\boldsymbol{\text{Yes}}$.
• 4) Scattered points: No vertical line intersects more than one point. Passes the vertical line test. $\boldsymbol{\text{Yes}}$.

2. Tables/Mappings (Is it a function?):

• 5) Table: Input $x=4$ has two outputs ($8$ and $-2$). Fails the “one input → one output” rule. $\boldsymbol{\text{No}}$.
• 6) Mapping (oval diagram): Input $9$ maps to two outputs, and input $-6$ maps to two outputs. Fails the “one input → one output” rule. $\boldsymbol{\text{No}}$.
• 7) Input-Output Table: Each input ($0, 2, 4, 6$) has exactly one output. Passes the rule. $\boldsymbol{\text{Yes}}$.
• 8) Input-Output Table: Inputs $3, 5, 7$ each have one output (note: $5$ and $7$ map to $4$ and $6$—multiple inputs can share an output, but each input has only one output). Passes the rule. $\boldsymbol{\text{Yes}}$.

3. Ordered Pairs (Is it a function?):

• First set: $\{(5, -1), (0, 3), (-2, -4), (6, -1), (-2, 3)\}$: Input $-2$ has two outputs ($-4$ and $3$). Fails the “one input → one output” rule. $\boldsymbol{\text{No}}$.
• Second set: $\{(9, 2), (-4, -1), (0, -3), (-7, 6), (5, -2)\}$: Each input ($9, -4, 0, -7, 5$) has exactly one output. Passes the rule. $\boldsymbol{\text{Yes}}$.

Final Answers (Summarized):

Item	Is it a function?
2)	No
3)	Yes
4)	Yes
5)	No
6)	No
7)	Yes
8)	Yes
First ordered pair set	No
Second ordered pair set	Yes

(Note: If you need only specific items, adjust based on the question’s focus. The key is applying the vertical line test or “one input → one output” rule.)