For each of the following relations, explain why they are or are not a function using complete sentences. (2 points per section)
A.
x y
0 2
4 18
5 27
7 51
B.
x -2 -1 0 -1
y 3 6 9 12
C. Domain: The ages of the students in GACA's 9th grade; Range: The number of siblings they have.
A. This relation is a function because each input (x-value) corresponds to exactly one output (y-value). For example, when x=0, y=2, when x=4, y=18, when x=5, y=27, and when x=7, y=51. There are no repeated x-values with different y-values.
B. This relation is not a function because for x=-1, there are two different y-values, specifically y=6 and y=12. This violates the definition of a function where each input must have exactly one corresponding output.
C. This relation is a function because each student's age in the 9th grade corresponds to a specific number of siblings they have. Each unique age corresponds to a unique number of siblings, and there are no repeated ages with different numbers of siblings.