Question

8) The relationship defined by the set of ordered pairs {(1,2).(3,4),(5,6),(1,9)} is not a function. Which of the ordered pairs listed below, when omitted from this set, will make the resulting set a function? a) (1,2) b) (3,4) c) (5,6) d) (1,9)

Answer 1

Let's begin by listing out the information given to us:

$\mleft\{\mleft(1,2\mright).\mleft(3,4\mright),\mleft(5,6\mright),\mleft(1,9\mright)\mright\}$

When we observe the ordered pairs closely, we will see a trend:

$\begin{gathered} (x,y)=(x,x+1);y=x+1 \\ (1,2)=(1,1+1) \\ (3,4)=(3,3+1) \\ (5,6)=(5,5+1) \\ (1,9)=(1,1+8) \\ \\ \therefore(1,9)\text{ is the anomaly} \end{gathered}$

When (1, 9) is omitted from the set, these ordered pairs become a function. Hence, option d is the correct answer