Which relation(s) best shows Y as a function of X? Make 2 piles function or not a function. Drag each card to determine if it is a function or not. which one is a function and which one isn't?

Question

x,y
-1,3
2,0
5,3
8,6

x,y
3,-1
3,0
3,1
3,2

x,y
-1,3
0,3
1,3
2,3

x,y
4,3
3,0
3,1
2,4

input, output
2, 20
4, 30
3, 40

input, output
10, 15
20, 25
30, 35
40, 45

Answer 1

To determine if a relation is a function, we need to check if each input (or x-value) maps to exactly one output (or y-value). If an input is associated with multiple outputs, then it is not a function.

Let's evaluate each relation:

1. Relation:

   x,y
   -1,3
   2,0
   5,3
   8,6
   

   • Each x-value is unique. This is a function.

2. Relation:

   x,y
   3,-1
   3,0
   3,1
   3,2
   

   • The x-value 3 corresponds to multiple y-values (-1, 0, 1, 2). This is not a function.

3. Relation:

   x,y
   -1,3
   0,3
   1,3
   2,3
   

   • Each x-value is unique, even though they all yield the same y-value (3). This is a function.

4. Relation:

   x,y
   4,3
   3,0
   3,1
   2,4
   

   • The x-value 3 corresponds to multiple y-values (0, 1). This is not a function.

5. Relation:

   input, output
   2, 20
   4, 30 
   3, 40
   

   • Each input is unique. This is a function.

6. Relation:

   input, output
   10, 15
   20, 25
   30, 35
   40, 45
   

   • Each input is unique. This is a function.

Summary:

Functions:

• 1st relation
• 3rd relation
• 5th relation
• 6th relation

Not Functions:

• 2nd relation
• 4th relation