Question

homework #1 no work= no credit! explain your reasoning for each answer!

1. which table represents a function?

(1)

x	2	4	2	4
f(x)	3	5	7	9

(3)

x	3	5	7	9
f(x)	2	4	2	4

(2)

x	0	-1	0	1
f(x)	0	1	-1	0

(4)

x	0	1	-1	0
f(x)	0	-1	0	1

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (f(x) - value). So we need to check each table to see if any x - value is repeated with different f(x) - values.

Step2: Analyze Table (1)

In Table (1), the x - values are 2, 4, 2, 4. For x = 2, we have f(x)=3 and f(x)=7 (since x = 2 appears twice with different f(x) values). For x = 4, we have f(x)=5 and f(x)=9. So this is not a function.

Step3: Analyze Table (3)

In Table (3), the x - values are 3, 5, 7, 9. Each x - value (3, 5, 7, 9) appears only once. So each input has exactly one output. Let's check: x = 3 gives f(x)=2, x = 5 gives f(x)=4, x = 7 gives f(x)=2, x = 9 gives f(x)=4. Even though different x - values can have the same f(x) - value, as long as each x has only one f(x), it's a function.

Step4: Analyze Table (2) (the third table, let's assume it's (2))

In Table (2), the x - values are 0, - 1, 0, 1. For x = 0, we have f(x)=0 and f(x)= - 1 (since x = 0 appears twice with different f(x) values). So this is not a function.

Step5: Analyze Table (4)

In Table (4), the x - values are 0, 1, - 1, 0. For x = 0, we have f(x)=0 and f(x)=1 (since x = 0 appears twice with different f(x) values). So this is not a function.

Answer:

(3) The table with x - values 3, 5, 7, 9 and f(x) - values 2, 4, 2, 4 (i.e., the table labeled (3)) represents a function because each x - value is unique (or each input x has exactly one output f(x)).