Answer:
1) NO
2) YES
3) YES
4) YES
Step-by-step explanation:
A function is a relation that maps elements from a set (the domain, the set of the inputs) into elements from another set (the range, the set of the outputs).
The condition for a function is that each element in the domain can be mapped into only one element in the range.
(Or each input can be mapped into only one output).
Now let's apply this theory to the exercises here.
In all the cases we have relations, so we need to check if one (or more) of the inputs is mapped into more than one output.
Also remember that in the point notation (x, y) the first value is the input and the second is the output.
1)
Here we can see the points (-1, 5) and (-1, 2)
So the input -1 is mapped into two different outputs, 5 and 2.
This means that this is not a function.
2)
In this case, we can see that all the inputs are different (1, -2, 3, 5), so this is a function.
3)
Again, here we can see that each input is being mapped into only one output, then this is a function.
4)
In a graph, the horizontal position represents the input value and the vertical position represents the output value.
One way to tell if a graph belongs to a function or not, is to see if there is a vertical line such that more than one point intersects that line. If that happens, then we have two points with the same input value but different output value and the relation is not a function.
In this case, we can see that this does not happen, and then we can conclude that the graph represents a function.
