Question

Plot the points $(1,5),(2,6),(3,9),(1,12)$in the Cartesian plane. Is the relation $\left\{\right(1,5),(2,6),(3,9),(1,12\left)\right\}$a function? Why?

Short answer

The points $(1,5),(2,6),(3,9),(1,12)$in the Cartesian plane is shown below:

The relation $\left\{\right(1,5),(2,6),(3,9),(1,12\left)\right\}$is not a function since there are two ordered pairs, $(1,5)$and $(1,12)$, in which each element in the domain does not correspond to exactly one element in the range.

Step-by-step solution

Step 1. Given information

Plot the points $(1,5),(2,6),(3,9),(1,12)$in the Cartesian plane as shown below:

Step 2. Explain whether the relation {(1, 5),(2, 6),(3, 9),(1, 12)} represents a function.

A function is said to be a relation if each element of X corresponds to exactly one element of Y, where the set X is called the domain and set Y is called the range of the function.

Assume a relation$\left\{\right(1,5),(2,6),(3,9),(1,12\left)\right\}$.

Conclude from the given relation that it is not a function since there are two ordered pairs, $(1,5)$and $(1,12)$, in which each element in the domain does not correspond to exactly one element in the range.