Question

Which is a function?

a.) {(1000, 10), (1000, 12), (1000, 16), (100, 5), (100, 7), (78, 3), (90, 5)}
b.) {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
c.) {(6, 3), (5, 2), (4, 1), (3, 0), (4, –1), (5 ,–2), (6 ,–3)}
d.) {(7, 2), (100, 10), (13, –7), (7, 9), (10, 100), (4, –2), (5, 5)}

Answer 1

Therefore, the only option that is a function is b.) {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}.

Step-by-step explanation:

A function is a relation between two sets, where each element in the first set (domain) is associated with exactly one element in the second set (codomain). In other words, for each input (x-value), there is exactly one output (y-value).

Checking each option:

a.) {(1000, 10), (1000, 12), (1000, 16), (100, 5), (100, 7), (78, 3), (90, 5)}

This option is not a function because the input value 1000 has multiple corresponding output values (10, 12, and 16).

b.) {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}

This option is a function because each input value has a unique corresponding output value.

c.) {(6, 3), (5, 2), (4, 1), (3, 0), (4, –1), (5 ,–2), (6 ,–3)}

This option is not a function because the input value 4 has multiple corresponding output values (1 and -1).

d.) {(7, 2), (100, 10), (13, –7), (7, 9), (10, 100), (4, –2), (5, 5)}

This option is not a function because the input value 7 has multiple corresponding output values (2 and 9).

Answer 2

A function is a relation between a set of inputs and outputs, where each input is associated with exactly one output. Option b is the only one that represents a function.

Step-by-step explanation:

A function is a relation between a set of inputs (called the domain) and a set of outputs (called the range), where each input is associated with exactly one output. In order for a relation to be a function, each input value must be paired with exactly one output value.

Looking at the options given:

a.) {(1000, 10), (1000, 12), (1000, 16), (100, 5), (100, 7), (78, 3), (90, 5)}

b.) {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}

c.) {(6, 3), (5, 2), (4, 1), (3, 0), (4, –1), (5 ,–2), (6 ,–3)}

d.) {(7, 2), (100, 10), (13, –7), (7, 9), (10, 100), (4, –2), (5, 5)}

Option b is a function because each input value is paired with exactly one output value.