Chapter 4.4, Problem 35PPE

To determine

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

Answer to Problem 35PPE

This relationship should be represented by continuous graph.

Explanation of Solution

Given information:

The area $A$ of an isosceles right triangle depends on the length $\mathcal{l}$ of each leg of the triangle. This is represented by the rule $A=\frac{1}{2}{\mathcal{l}}^2$

Calculation:

Consider area of isosceles right triangle is represented by $A$ and length of each leg of isosceles right triangle is represented by $\mathcal{l}$ .

Since $A$ depends on $\mathcal{l}$ . So this gives function rule

  $A=\frac{1}{2}{\mathcal{l}}^2$

Make table of values using this function rule. Choose any $\mathcal{l}$ value. Substitute in function rule and solve for $A$ value. Table is as follows:

$\mathcal{l}$	0	1	2	3	4
$A$	0	0.5	2	4.5	8

Graph each ordered pair $\left(\mathcal{l},A\right)$ . Graph is as follows. In this graph horizontal axis represents length of each leg of isosceles right triangle and vertical axis represents area of isosceles right triangle-

  

Thus, this relationship should be represented by continuous graph because after observing the graph found that, for any length value can find area of isosceles triangle.