Question

The points on the graphs represent relations. Classify these relations according to whether or not they are functions.

Answer 1

Answer:

A function $f$ from a set $A$ to a set $B$ is a relation that assigns to each element $x$ in the set $A$ exactly one element $y$ in the set $B$. The set $A$ is the domain (also called the set of inputs) of the function and the set $B$ contains the range (also called the set of outputs).

• First figure is not a function because the x-coordinate 2 has more than one element in the set of outputs.

• Second figure is a function because this each element $x$ in the set $A$ is assigned to exactly one element $y$ in the set $B$.

• Third figure is not a function because the x-coordinates -1, 1 and 2 have assigned more than one element in the set of outputs.

• Fourth figure is a function because this each element $x$ in the set $A$ is assigned to exactly one element $y$ in the set $B$.