Question

Given the relation: (0,0), (5,10), (6,12), (10,20), and based on the definition of a function, is that relation a function? Why or why not?

a) Yes, it is a function because each input has a unique output.
b) No, it is not a function because there are repeated inputs.
c) Yes, it is a function because the outputs are evenly spaced.
d) No, it is not a function because the outputs do not follow a pattern.

Answer 1

The relation given is a function because each input has a unique output, adhering to the definition of a function.

Step-by-step explanation:

The relation you've mentioned: (0,0), (5,10), (6,12), (10,20), is indeed a function. A function is a special type of relation where each input (x-value) is associated with exactly one output (y-value). In this relation, every x-value has a unique corresponding y-value. For example, 0 is paired with 0, 5 is paired with 10, and so on.

Therefore, the correct choice is: a) Yes, it is a function because each input has a unique output.

The definition of a function fits perfectly with what we see in the relation provided. There aren't any repeated inputs, so there's no way for the same input to have two different outputs.