Initial Test - Functions and Non-Functions

Which of the following relations is a function?

• Every student → height

• Every student → their parent's name

• Every student → student ID and attendance number at the same time

• Every student → hobby

Given the set A = {1, 2, 3} and B = {a, b, c}. The relation R = {(1,a), (2,b), (3,c)}. Is R a function?

• Yes, because every member of A is paired with exactly one member of B

• No, because there are members of A paired with more than one

• No, because there are members of B paired with more than one

• No, because A and B are not the same size

The relation student → their date of birth is included in ...

• Function, because every student has exactly one date of birth

• Function, because every student can have more than one date of birth

• Not a function, because many students have the same date of birth

• Not a function, because a student may not have a date of birth

Arrow diagram: A = {2, 3, 4}, B = {4, 9, 16} with the rule f(x) = x². The correct pairs are ...

• (2,4), (3,9), (4,16)

• (2,3), (3,4), (4,5)

• (2,9), (3,16), (4,4)

• (2,16), (3,9), (4,4)

From the following graph (for example, a parabola y = x²), is the relationship x → y a function?

• Yes, because every value of x has exactly one value of y

• No, because there are x values paired with two y values

• No, because y can be negative

• Yes, because the parabola graph is U-shaped

The relation 'mother → her biological child' is included in ...

• Function, because every mother has exactly one child

• Function, because every mother can have many children

• Not a function, because one mother can have more than one child

• Not a function, because not everyone has children

The relation 'motor vehicle → its license plate' is included in ...

• Function, because every vehicle has a unique license plate

• Not a function, because one vehicle can have many license plates

• Not a function, because there are vehicles with the same plate

• Function, because a vehicle may not have a plate

If f : x → 2x + 1, determine f(3).

• 5

• 6

• 7

• 8

Set A = {a, b, c}, B = {1, 2}. The relation R = {(a,1), (b,1), (c,2)}. Is R a function?

• Yes, because every member of A is paired with exactly one member of B

• No, because not all members of B are paired

• No, because members of A are paired with more than one

• No, because many members of B are the same

Observe the following diagram: A = {1, 2, 3}, B = {a, b, c}, with pairs (1,a), (2,b), (3,b). Is this relation a function?

• Yes, because every member of A is paired with exactly one member of B

• No, because there are members of A paired with more than one

• No, because there are members of B that are not paired

• No, because the number of A and B is not the same