Question

Determine whether each table represents an inverse variation. Explain.

Short answer

A table represents an inverse variation.

Step-by-step solution

Step 1. Inverse variation.

$y$varies inversely as$x$ if there is some nonzero constant$k$ such that $xy=k$, where$x\ne 0$ and $y\ne 0$.

Step 2. Find xy.

Find $xy$for each ordered pair.

$$\begin{gathered} 2\cdot 2=4 \\ 4\cdot 1=4 \\ 8\cdot \frac{1}{2}=4 \end{gathered}$$

Step 3. Write the conclusion.

As$xy$ is constant, the table represents an inverse variation.