Q42. - Algebra 2

Question

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.

Write a relation to represent the data.

Step-by-Step Solution

Answer

The required relation for the given data is $\left\{\left(1987,12\right),\left(1989,13\right),\left(1991,11\right),\left(1993,12\right),\left(1995,9\right),\left(1997,6\right),\left(1999,3\right)\right\}$.

Step 1 – Definition of a relation.

A relation is the set of ordered pairs $\left(x,y\right)$, where $x$ is the input value and $y$ is the output value.

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 – Write the relation in ordered pairs.

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 $12,13,11,12,9,6,3$.

 

The ordered pairs for the given data are $\left(1987,12\right),\left(1989,13\right),\left(1991,11\right),\left(1993,12\right),$ $\left(1995,9\right),\left(1997,6\right)$and $\left(1999,3\right)$.

Thus, the required relation for the given data is$\left\{\left(1987,12\right),\left(1989,13\right),\left(1991,11\right),\left(1993,12\right),\left(1995,9\right),\left(1997,6\right),\left(1999,3\right)\right\}$.