Chapter 1.7, Problem 29PPE

To determine

To find the domain and range of the relation and check if the relation is function or not.

Answer to Problem 29PPE

Domain: $\left\{0,1,2,3\right\}$

Range: {2.3,6,9.7,13.4}

Explanation of Solution

Given:

A bird feeder will hold up to 3 quarts of seed. The feeder weighs 2.3 pounds when empty and 13.4 pounds when full.

In order to find the domain and range, first establish a relation between them.

As it is mentioned, when there is no quartz of seed in the bird feeder, the bird feeder weighs 2.3 pounds and when there is 3 quarts of seeds, the bird feeder weighs 13,4 pounds when full.

So, by using unitary method,

3 quarts of seed $\to$ $(13.4-2.3)=11.1$ pounds

1 quart of seed $\to$ 3.7 pounds

This means for every quarts there will be a rise of 3.7 pounds.

So the relation will be: Weight of bird feeder = 2.3 + (3.7 $\times$ quarts of seed)

Now, the tabulated data is:

Domain (Quarts of seed)	Range (Weight of bird feeded in pounds)
0	2.3
1	$2.3+\left(1\times 3.7\right)=6$
2	$2.3+(2\times 3.7)=9.7$
3	$2.3+(3\times 3.7)=13.4$

Graph:

Now, draw a graph by using above table of values.

x-axis represents the Quarts of seed.

y-axis represents the Weight of bird feeded in pounds.

  

In order to check if a relation is a function or not, vertical line method is applied.

If a vertical line can be drawn through the graph and the line meets the graph at only one point, the function is said to be one to one.

When a vertical line is drawn through this graph, it cuts the graph at only one point. It is clear that all the values of x in the domain has a unique value of y.

Hence, it can be concluded that above relation is a function.

Conclusion:

Therefore, given relation is a function and

Domain: $\left\{0,1,2,3\right\}$ and Range: {2.3,6,9.7,13.4}.