Question

what did farmer john show his chicken when she wouldnt lay any eggs? determine whether each relation is a function. indicate whether it is a function or is not a function by circling the appropriate letter in the chart. the answer to the title question is found by reading the circled letters in the top row, then the circled letters in the bottom row. 1. {(-1,8), (0,15), (1,-4), (2,0)} 2. {(-2,7), (6,2), (-2,-3), (0,9)} 3. {(-5,2), (5,2), (0,-3), (3,-8), (-7,4), (-1,-1)} 4. {(-7,2), (4,-6), (2,-2), (-3,9), (0,-11), (4,0)} 5.

x	y
-6	4
-4	0
-2	-5
0	-5
2	0
4	4	6.
x	y
8	7
-3	16
-9	0
15	33
-1	-1
-9	-6	7.
x	y
5	18
-2	-2
0	12
12	0
-40	17
-5	18	8.
x	y
-1	78
0	80
1	85
0	90
-1	95	9. graph of a relation 10. graph of a relation 11. graph of a relation 12. graph of a relation 13. graph of a relation 14. graph of a relation is a function > a r q e o l o f d e g o g q not a function > i s t a t m e p o l a l l e

Explanation:

Step1: Recall function definition

A relation is a function if for each input (x - value) there is exactly one output (y - value).

Step2: Analyze set - based relations

1. For $\{(-1,8),(0,15),(1, - 4),(2,0)\}$, each x - value has a unique y - value, so it is a function.
2. For $\{(-2,7),(6,2),(-2,-3),(0,9)\}$, the x - value $x=-2$ has two different y - values ($y = 7$ and $y=-3$), so it is not a function.
3. For $\{(-5,2),(5,2),(0,-3),(3,-6),(-7,4),(-1,-1)\}$, each x - value has a unique y - value, so it is a function.
4. For $\{(-7,2),(4,-6),(2,-2),(-3,9),(0,-11),(4,0)\}$, the x - value $x = 4$ has two different y - values ($y=-6$ and $y = 0$), so it is not a function.

Step3: Analyze table - based relations

1. In the first table, each x - value has a unique y - value, so it is a function.
2. In the second table, each x - value has a unique y - value, so it is a function.
3. In the third table, each x - value has a unique y - value, so it is a function.
4. In the fourth table, the x - value $x = 0$ has two different y - values ($y = 50$ and $y=90$), so it is not a function.

Step4: Analyze graph - based relations

1. Using the vertical - line test, the graph passes the vertical - line test (any vertical line intersects the graph at most once), so it is a function.
2. Using the vertical - line test, the graph passes the vertical - line test, so it is a function.
3. Using the vertical - line test, the graph passes the vertical - line test, so it is a function.
4. Using the vertical - line test, a vertical line can intersect the graph at more than one point, so it is not a function.
5. Using the vertical - line test, the graph passes the vertical - line test, so it is a function.
6. Using the vertical - line test, a vertical line can intersect the graph at more than one point, so it is not a function.

Step5: Find the answer to the riddle

Reading the circled letters in the top row and then the bottom row: "A R O E O L O F D E G O G Q" gives "A ROOFING".

Answer:

A ROOFING