Q56. - Algebra 2

Question

WRITING IN MATH Answer the question that was posed at the beginning of the lesson.

How do relations and functions apply to biology?

Include the following in your answer:

• An explanation of how a relation can be used to represent data, and
• A sentence that includes the words average lifetime, maximum lifetime, and function.

Step-by-Step Solution

Answer

• A relation represents a data in a set of ordered pairs.
• The required sentence is “The relation between the average lifetime and the maximum lifetime is not a function”.

Step 1 – Table for the relation.

The table shows the average lifetime and maximum lifetime for some animals

The ordered pairs for the above data are $\left(12,38\right),\left(15,30\right),\left(8,20\right),\left(12,20\right),\left(20,50\right)$. The set of these ordered pairs $\left\{\left(12,38\right),\left(15,30\right),\left(8,20\right),\left(12,20\right),\left(20,50\right)\right\}$ represents a relation for the data related to biology.

In these ordered pairs the first number represents the average lifetime (years) and Maximum lifetime (years)

Step 2 – The graph for the relation.

Plot the ordered pairs $\left(12,38\right),\left(15,30\right),\left(8,20\right),\left(12,20\right),\left(20,50\right)$ on a coordinate plane to get the graph.

In the above graph, the vertical axis represents the maximum lifetime. The horizontal axis repesents the average lifetime

Step 3 – Check whether the relation is a function or not.

From the above table and graph it is clear that $12$ in the domain is paired with $20$ and $28$ in the range.

 The above relation is not a function because each element of the domain is not related to only one element of the range.

 Thus, the relation between the average lifetime and the maximum lifetime is not a function.