Q45. - Algebra 2

Question

GOVERNMENT For Exercises $42-45$, use the table below that shows the number of members of the U.S. House of Representatives with $30$ or more consecutive years of service in Congress from 1987 to 1999.

$45.$ Is the relation a function? If so, is it a one-to-one function? Explain.

Step-by-Step Solution

Answer

The relation is a function but not one-to-one function.

Step 1 – Definition of function and one-to-one function.

A relation is a function if each element of the domain is paired with exactly one element of the range.

A relation is not a function if there exist an element in the domain paired with more than one element of the range.

In a function is called one-to-one if each element of the range is paired with exactly one element of the domain.

 

Step 2 – Given information.

The table below shows the number of members of the U.S. House of Representatives with $30$  or more consecutive years of service in Congress from $1987 to 1999$.

Step 3 – Graph the given relation.

It is given that the years are the domain and the representatives are range. So, the input values are $1987,1989,1991,1993,1995,1997,1999$ and the respective output values are $12,13,11,12,9,6,3$.

For each element of the domain is paired with exactly one element of the range. So, the given relation is a function.

In the given function $1987$ and $1993$ both are paired with $12$. Since each element of the range is paired more than one element of the domain, therefore the function is not one-to-one.

 Thus, the relation is a function but not one-to-one function.