Question

Determine whether the table represents an inverse variation. Explain.

$\mathit{x}$	$\mathit{y}$
2	8
4	4
8	2
16	1

Short answer

The given table represents an inverse variation.

Step-by-step solution

Step 1. Define the meaning of variation.

The changing of variable parameters is called a variation.

Step 2. Define the inverse variation.

The inverse variation of two variables $x$and $y$is given by

$xy=k$

Here, $k$is called the constant of variation.

Step 3. Determine whether the given table represents an inverse variation. 

Observe the table.

$\begin{array}{c}2\times 8=16\\ 4\times 4=16\\ 8\times 2=16\\ 16\times 1=16\end{array}$

Since the product $xy$is a constant, so it represents an inverse variation.

Therefore the given table represents an inverse variation.