a A function is a relationship that pairs each input value with exactly oneoutput value.
B
b A function is a relationship that pairs each input value with exactly one output value.
C
c A function is a relationship that pairs each input value with exactly one output value.
A
a Yes, see solution.
B
b Yes, see solution.
C
c No, see solution.
Practice makes perfect
a To determine if a relation is a function, we must keep in mind the definition of a function.
Function
A function is a relationship that pairs each input value with exactly one output value.
Let's now analyze the given set of ordered pairs.
( 0, 0), ( 1, 1), ( 2, 2), ( 3, 3), ( 4, 4)
We can see that for every input x, there is a unique output y. Therefore, the relation is a function. We can verify our answer by performing the Vertical Line Test on the graph of the ordered pairs.
Since the vertical lines intersect the relation one time each, the relation is a function.
b Now we will determine whether the second relation is a function.
( 0, 8), ( 1, 6), ( 2, 4), ( 3, 2), ( 4, 0)
We see that for every input x there is a unique output y. Therefore, the relation is a function. This can be visualized performing the Vertical Line Test.
Since the vertical lines intersect the relation one time each, the relation is a function.
c Finally, we will repeat the same process for the last set of ordered pairs.
( 3, 0), ( 3, 1), ( 3, 2), ( 3, 3), ( 3, 4)
In this set, there is only one input and many outputs. Therefore, the relation is not a function. This can be visualized by performing the Vertical Line Test.
Since the vertical line intersects the relation more than once, the relation is not a function.
