Question

Analyze both the graphs and choose the correct statement.

Graph I



Graph II

Answer 1

Considering graph I:
Graph I consists of a set of ordered pairs $(x,y)$, Hence, it is a relation.
Look for any value(s) of $x$ that have more than one corresponding value of $y$.
$x=3$ has more than one corresponding value of y, i.e., $y=1$ and $y=3$.
Each input ($x$) of Graph I does not have a unique output ($y$), as one input has two outputs, i.e., $(3,1)$ and $(3,3)$. Hence, Graph I is a relation, but not a function.

Considering graph II:
Graph II consists of a set of ordered pairs $(x,y)$. Hence, it is a relation.
Look for any value(s) of $x$ that have more than one corresponding value of $y$.
As the graph represents a straight line that is not vertical, there is no value of $x$ that will have more than one corresponding value of $y$.
Each input ($x$) of Graph II has a unique output ($y$).
Hence, Graph II is a function.