X as 1,2,3,4,5 has no repeats, and Y as 6,9,7,11,8 also has no repeats.
So that means that the relation is
X 1 | 2 | 3 | 4 | 5 |
Y 6 | 9 | 7 |11 | 8 |
This is the set of ordered pairs:
{ (1,6), (2,9), (3,7), (4,11), (5,8) }
And so the graph of the relation looks like this:
When you plot them, you don't get a line or a curve, but just the 5 isolated
points plotted above.
You spoke of "a graph LINE". But there is no graph LINE at all.
Maybe you thought that the points had to be connected with LINES or maybe a
curved line like one of these:
But neither of those two graphs is the graph of the given relation. That's why
I X-ed them out. The points are NOT connected at all, but are separate points.
What you wrote:
"And yet a horizontal line will pass through the graph twice, Ie, between 6
and 9 is 7."
is false. That's because no horizontal line will pass through more than
ONE of the 5 points. That's why it's one-to-one. Look at these green horizontal
lines below:
Not a one of those horizontal green lines goes through more than ONE point. Some
horizontal lines go through 1 point and some go through NO points. But no
horizontal line can pass through more than one of the points of the relation. So
the relation is one-to-one.
Edwin