a If a relation is a function, how many y-values can an x-value have?
B
b If a relation is a function, how many y-values can an x-value have?
C
c If a relation is a function, how many y-values can an x-value have?
A
a Yes, see solution.
B
b No, see solution.
C
c No, see solution.
Practice makes perfect
a For a relation to be a function, each x-value can only be paired with one y-value, but one y-value can be paired with multiple x-values. In a graph we can check if each x-value has only one y-value by subjecting it to the Vertical Line Test.
On the given graph there is no visible part where two points have the same y-value. Each vertical line passes through the graph at only one point, so the graph is a function.
b For a relation to be a function, each x-value can only be paired with one y-value, but one y-value can be paired with multiple x-values. In a graph, we can check if each x-value has only one y-value by subjecting it to the Vertical Line Test.
Observing the graph, we can see that there is more than one x-value with more than one y-value. The relation fails the Vertical Line Test, so the graph is not a function.
c For a relation to be a function, each x-value can only be paired with one y-value, but one y-value can be paired with multiple x-values. In a graph, we can check if each x-value has only one y-value by subjecting it to the Vertical Line Test.
Observing the graph, we can see that there is at least one x-value with more than one y-value. The relation fails the Vertical Line Test, so the graph is not a function.
