Answer:
Question 1:
The set {(1, 2), (2, -3), (3, 4), (4, -5)} represents y as a function of x
Question 2:
The best statement describes the relation is "The relation represents y as a function of x, because each value of x is associated with a single value of y" ⇒ 3rd answer
Question 4:
There are missing options so we can not find the correct answer
Question 5:
The sets {(1 , 1), (2 , 2), (2 , 3)} and {(1, 2), (1, 3), (1, 1)} do not represent y as a function of x ⇒ 1st and 4th answers
Step-by-step explanation:
The relation is a function if each value of x has <em>ONLY</em> one value of y
Ex: The set {(3 , 5) , (-2 , 1) , (4 , 3)} represents y as a function of x because x = 3 has only y = 5, x = -2 has only y = 1, x = 4 has only y = 3
The set {(4 , 5) , (-2 , 1) , (4 , 3)} does not represent y as a function of x because x = 4 has two values of y 5 and 3
Now Let us solve the questions
Question 1:
∵ The set is {(1 , 3), (1 , 5), (1 , 7), (1 , 9), (1 , 11)}
∵ x = 1 has values of y = 3, 5, 7, 9, 11
- That means not each x has only one value of y
∴ The set does not represent y as a function of x
∵ The set is {(2 , 3), (3 , 5), (3 , -5), (-2 , 8), (-2 , -8)
∵ x = 3 has values of y = -5, 5 and x = -2 has values of y = -8, 8
- That means not each x has only one value of y
∴ The set does not represent y as a function of x
∵ The set is {(1, 2), (2, -3), (3, 4), (4, -5)}
∵ x = 1 has only y = 2
∵ x = 2 has only y = -3
∵ x = 3 has only y = 4
∵ x = 4 has only y = -5
- That means each x has only one value of y
∴ The set represents y as a function of x
∵ The set is {(1 , 2), (2 , 3), (3 , 4), (3 , 5)}
∵ x = 3 has values of y = 4, 5
- That means not each x has only one value of y
∴ The set does not represent y as a function of x
Question 2:
∵ The relation is (3, 4), (4, 3), (6, 3), (7, 8), (5, 4)
∵ x = 3 has only y = 4
∵ x = 4 has only y = 3
∵ x = 6 has only y = 3
∵ x = 7 has only y = 8
∵ x = 5 has only y = 4
- That means each x has only one value of y
∴ The relation represents y as a function of x, because each
value of x is associated with a single value of y
Question 4:
The first representation
→ x : y
→ 3 : 3
→ 5 : 3
→ 7 : 3
→ 9 : 3
∵ x = 3 has only y = 3
∵ x = 5 has only y = 3
∵ x = 7 has only y = 3
∵ x = 9 has only y = 3
- That means each x has only one value of y
∴ The representation represents y as a function of x
The second representation
→ x : y
→ -2 : 6
→ -3 : -7
→ 5 : 1
→ 4 : 6
∵ x = -2 has only y = 6
∵ x = -3 has only y = -7
∵ x = 5 has only y = 1
∵ x = 4 has only y = 6
- That means each x has only one value of y
∴ The representation represents y as a function of x
The other two options are missing so we can not find the answer
Question 5:
∵ The set is {(1 , 1), (2 , 2), (2 , 3)}
∵ x = 2 has y = 2 and 3
- That means one value of x has more than one value of y
∴ The set does not represent y as a function of x
∵ The set is {(1, 2), (2, 3), (3, 3)}
∵ x = 1 has only y = 2
∵ x = 2 has only y = 3
∵ x = 3 has only y = 3
- That means each x has only one value of y
∴ The representation represents y as a function of x
∵ The set is {(1, 1), (2, 1), (3, 1)}
∵ x = 1 has only y = 1
∵ x = 2 has only y = 1
∵ x = 3 has only y = 1
- That means each x has only one value of y
∴ The representation represents y as a function of x
∵ The set is {(1, 2), (1, 3), (1, 1)}
∵ x = 1 has y = 2, 3, and 1
- That means one value of x has more than one value of y
∴ The set does not represent y as a function of x
