Question

3. Look at the set of ordered pairs below. Determine if the three statements that follow are true or false.

If it is true, explain why you know that it is true.
If it is false, explain why you know that it is false and change the statement to a true statement.
{(3,6), (4,6), (5,7), (6,8), (7,10), (8,10)
Statement 1:
The relation is not a function because every y-value has more than one corresponding X-value
Statement 2:
The domain of this relation is 3=< x =< 8.
Statement 3:
The range of this relation is {6, 7, 8, 10}

Answer 1

Statement 1 - false

A function is one-to-one or many-to-one.

One-to-one means each value in the range (y-values) corresponds to exactly one value in the domain (x-values)

Many-to-one means some values in the range (y-values) correspond to more than one (many) value in the domain (x-values).

Therefore, as some y-values correspond to more than one x-value, this is a many-to-one function.

The true statement should be:

The relation is a function because some y-values correspond to more than one x-value.

Statement 2- true

The domain is the set of input values (x-values). Therefore, the domain is 3 ≤ x ≤ 8 as the smallest x-value is 3 and the highest x-value is 8.

Statement 3 - true

The range is the set of output values (y-values). Therefore, the range is {6, 7, 8, 10} as these are the y-values of the ordered pairs.