Q 1. - Precalculus Enhanced with Graphing Utilities

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?

Step-by-Step Solution

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 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.