Question

name
date
hour
functions - 1
determine if the following represent functions.
1)
2)
3)
4)
5)
6)

1. {(8, 2) (3, 4) (6, 5) (3, 6)}
2. {(-4, 2) (3, 3) (8, 4) (4, 6)}
3. {(-8, 2) (8, 3) (8, 4) (12, 4)}

10)
11)
12)

Explanation:

Step1: Recall function definition

A relation is a function if each input has exactly one output. For graphs, use the Vertical Line Test: any vertical line intersects the graph at most once.

Step2: Analyze mapping 1

Input 3 maps to B and C.
Conclusion: Not a Function

Step3: Analyze mapping 2

All inputs (1,2,3,4) have one output each.
Conclusion: Function

Step4: Analyze mapping 3

Input 2 maps to B and C.
Conclusion: Not a Function

Step5: Analyze graph 4

Vertical lines intersect the curve once.
Conclusion: Function

Step6: Analyze graph 5

Vertical lines intersect the line once.
Conclusion: Function

Step7: Analyze graph 6

A vertical line intersects the graph twice.
Conclusion: Not a Function

Step8: Analyze set 7

Input 3 maps to 4 and -6.
Conclusion: Not a Function

Step9: Analyze set 8

Input -4 maps to 2 and -6.
Conclusion: Not a Function

Step10: Analyze set 9

All inputs (-4,6,8,12) have one output each.
Conclusion: Function

Step11: Analyze graph 10

Vertical lines hit at most one point.
Conclusion: Function

Step12: Analyze graph 11

Vertical lines hit at most one point.
Conclusion: Function

Step13: Analyze graph 12

A vertical line hits two points.
Conclusion: Not a Function

Answer:

1. Not a Function
2. Function
3. Not a Function
4. Function
5. Function
6. Not a Function
7. Not a Function
8. Not a Function
9. Function
10. Function
11. Function
12. Not a Function