Chapter 4.4, Problem 22PPE

To determine

To sketch: the graph of the given function rule and to explain of intervals on the axes of the graph. To find whether the graph is continuous or discrete.

Answer to Problem 22PPE

This relationship should be represented by discrete graph.

Explanation of Solution

Given information:

The total weight $w$ , in pounds, of a tractor-trailer capable of carrying 8 cars depends on the number of cars $c$ on the trailer. This situation is represented by the function rule $w=37000+4200c$ .

Calculation:

Consider total weight a tractor trailer is represented by $w$ and number of cars on trailer is represented by $c$ .

Since $w$ depends on $c$ . So this gives function rule

  $w=37000+4200c$

Make table of values using this function rule. Choose any $c$ value. Substitute in function rule and solve for $w$ value. Table is as follows:

$c$	0	2	4	6	8
$w$	37000	45400	53800	62200	70600

Graph each ordered pair $\left(c,w\right)$ . Graph is as follows. In this graph horizontal axis represents number of cars and vertical axis represents total weight of tractor trailer -

  

Since there are maximum8 cars can place on tractor trailer. This is represented by inequality $0\le c\le 8$ . That’s why chosen any $c$ value between0 to 8.

Observe the graph. Found that each car has specific weight. So cannot place connect all points by the definition, discrete graph is composed of distinct, isolated points.

Thus, this relationship should be represented by discrete graph.