A relation is (also) a function if every input x is mapped to a unique output y.
In terms of graphical representation, this implies that a graph represents a function if there doesn't exist a vertical line that intersects the graph more than once. So:
- The first graph is exactly a vertical line, so it's not a function.
- The second graph represents the function y=x, so it's a function: you can see that every possible vertical line crosses the graph only once.
- The third graph is not a function, because you can draw vertical lines that cross the graph twice.
- Similarly, in the fourth graph you can draw vertical lines that cross the graph twice
- The fifth graph is a function, because every vertical line crosses the graph once
- The last graph is a function, although discontinuous, for the same reason.
They need to walk 2 dogs for the box of treats
Remainder theorem again...
So Yes, 
is a factor.
The number of people increased by 2.
This means as a ratio it is now 6/4 as many as originally planned.
6/4 can be reduced to 3/2.
The time and the number of people are inversely proportional, so the food would last 2/3 ( inverse is flipping the original ratio over) the original length of time.
This means the length of time the food lasts is reduced by 1/3, which is 33.3%
