a To test if a graph represents a function we can perform a Vertical Line Test. If we draw a vertical line anywhere in the diagram, it should only intercept the graph once.
As we can see, the drawn vertical line intercepts the graph once. If we were to draw the line along any other point in the diagram it would also intercept the graph only once. This means the relationship is a function.
b Let's perform the Vertical Line Test on the graph.
In this case the vertical line intercepts the graph at two points, which means it is not a function.
c The Vertical Line Test examines if there are any x-values that gives multiple y-values. If there are, the relationship is not a function. Examining the left column of the table, we see that there are no values of x that repeat. Therefore, this table does show a function.
d Like in Parts A and B, we will perform a Vertical Line Test to examine if the relationship is a function.
